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Essays on Institutions, Firm Funding and Sovereign
Debt
A thesis submitted to The University of Manchester for the Degree of
Doctor of Philosophy
in the Faculty of Humanities
2016
Adams Sorekuong Yakubu Adama
Department of Economics,
School of Social Sciences
Contents
Abstract 9
Declaration 10
Copyright Statement 11
Dedication 12
Acknowledgments 13
1 Thesis Introduction 15
2 Corruption and Political Turnover in a Sovereign Default Model 22
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.1.1 Related Literature . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2 Empirical Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2.1 Data Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2.2 Model Specification . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.3 The Theoretical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.3.1 The Government’s Decision Problem . . . . . . . . . . . . . . . 41
2.3.2 Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.3.3 Bond Price . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.3.4 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
1
2.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.4.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.4.2 Corruption, Political Risk and Default Risk . . . . . . . . . . . 49
2.4.3 Corruption, Welfare and Consumption . . . . . . . . . . . . . . 58
2.4.4 Characteristics of Debt and Spread around Defaults . . . . . . . 59
2.4.5 Output and Default . . . . . . . . . . . . . . . . . . . . . . . . . 62
2.4.6 Corruption, Political Turnover and Business Cycle Statistics . . 63
2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
2.6 Appendix A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
2.6.1 Computational Method . . . . . . . . . . . . . . . . . . . . . . 70
2.6.2 Consumption Equivalent Welfare Loss . . . . . . . . . . . . . . 71
2.7 Appendix B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
2.7.1 List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3 Limited Contract Enforcement and Firm Financing 77
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.2 Empirical Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.2.1 Data and Methodology . . . . . . . . . . . . . . . . . . . . . . . 82
3.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.3 The Investment Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.3.1 The Financial Contract . . . . . . . . . . . . . . . . . . . . . . . 87
3.3.2 The General Equilibrium Model . . . . . . . . . . . . . . . . . . 92
3.3.3 Calibration and Results . . . . . . . . . . . . . . . . . . . . . . 100
3.4 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
3.5 Appendix A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
3.5.1 Household Optimisation Problem . . . . . . . . . . . . . . . . . 117
3.5.2 Consumption-good Producing Firms . . . . . . . . . . . . . . . 118
3.5.3 The Entrepreneur . . . . . . . . . . . . . . . . . . . . . . . . . . 118
3.5.4 Optimal contract . . . . . . . . . . . . . . . . . . . . . . . . . . 119
3.5.5 Consumption Equivalent Welfare Loss . . . . . . . . . . . . . . 120
2
3.5.6 Steady State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
3.6 Appendix B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
3.6.1 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
3.6.2 Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
4 Thesis Conclusion 131
Bibliography 133
A Computer Codes 149
A.1 Chapter 2 Computer Codes . . . . . . . . . . . . . . . . . . . . . . . . 149
A.1.1 STATA CODES . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
A.1.2 FORTRAN CODES . . . . . . . . . . . . . . . . . . . . . . . . 152
A.1.3 MATLAB CODES . . . . . . . . . . . . . . . . . . . . . . . . . 216
A.2 Chapter 3 Computer Codes . . . . . . . . . . . . . . . . . . . . . . . . 228
A.2.1 STATA CODES . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
A.2.2 DYNARE CODES . . . . . . . . . . . . . . . . . . . . . . . . . 231
3
List of Tables
2.4.1.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.4.3.1 Average Consumption Equivalent Welfare Loss . . . . . . . . . . . . . . 59
2.4.5.1 Fraction of Default Episodes above Long-Run Mean . . . . . . . . . . . 63
2.4.6.1 Business Cycle Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.4.6.2 Default Risk Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
2.7.1.1 Sample of Defaulting and Debt Rescheduling Countries Used for Panel
Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
2.7.1.2 Variables for Empirical Work . . . . . . . . . . . . . . . . . . . . . . . . 73
2.7.1.3 Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
2.7.1.4 Probit models; dependent variable: Default - (excluding lagged default) 74
2.7.1.5 Probit models; dependent variable: Default - (excluding lagged default) 75
2.7.1.6 Probit models; dependent variable: Default - (including lagged default) 75
2.7.1.7 Mean Number of Defaults Given Change in Type . . . . . . . . . . . . 76
3.3.3.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
3.3.3.2 Productivity Shock . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
3.3.3.3 One-Time Wealth Transfer . . . . . . . . . . . . . . . . . . . . . . . 114
3.3.3.4 Welfare loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
3.3.3.5 Effect of Limited Enforcement and Monitoring Cost on Output . . . . . 115
3.6.1.1 Countries for Empirical Work . . . . . . . . . . . . . . . . . . . . . . . . 124
3.6.1.2 Continuation of Countries for Empirical Work . . . . . . . . . . . . . . 125
3.6.1.3 Summary statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
3.6.1.4 Fixed and Random Effects Regression for Full Sample(57 Countries) . . 127
4
3.6.1.5 Fixed and Random Effects Regression for Full Sample(57 Countries) . . 128
3.6.1.6 Fixed and Random Effects Regression(34 Countries) . . . . . . . . . . . 129
3.6.1.7 Fixed and Random Effects Regression (34 Countries) . . . . . . . . . . . 130
5
List of Figures
2.4.2.1 Value functions in a stable economy under less and more corrupt govern-
ments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.4.2.2 Default space against bond issuance and endowment . . . . . . . . . . . 53
2.4.2.3 Bond price for less corrupt government . . . . . . . . . . . . . . . . . . 55
2.4.2.4 Objective function of a less corrupt government . . . . . . . . . . . . . . 57
2.4.2.5 Optimal bond issuance . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.4.4.1 Average issuance level before and after a default . . . . . . . . . . . . . 60
2.4.4.2 Bond price faced by a more corrupt government . . . . . . . . . . . . . 61
2.4.4.3 Average spread before and after a default . . . . . . . . . . . . . . . . . 62
3.2.1.1 Scatter Plot of Real GDP, Credit Information and Contract Enforcement 83
3.2.1.2 Scatter: Standard Deviation of GDP and Contract Enforcement . . . . 84
3.3.3.1 Impulse responses from a positive technology shock. The vertical axis
measures percentage deviations from the steady state. The horizontal
axis measures time in quarters. . . . . . . . . . . . . . . . . . . . . . . 103
3.3.3.2 Relationship between expected leverage, expected risk premium and lim-
ited enforcement in response to productivity shocks. . . . . . . . . . . . 104
3.3.3.3 Impulse responses from a positive technology shock. The vertical axis
measures percentage deviations from the steady state. The horizontal
axis measures time in quarters. . . . . . . . . . . . . . . . . . . . . . . 105
3.3.3.4 Relationship between expected investment and limited enforcement in
response to productivity shocks. . . . . . . . . . . . . . . . . . . . . . . 106
6
3.3.3.5 Impulse responses from a negative shock to net worth. The vertical axis
measures percentage deviations from the steady state. The horizontal
axis measures time in quarters. . . . . . . . . . . . . . . . . . . . . . . 108
3.3.3.6 Relationship between expected leverage, expected risk premium and lim-
ited enforcement in response to net worth shocks. . . . . . . . . . . . . 109
3.3.3.7 Impulse responses from a negative shock to net worth. The vertical axis
measures percentage deviations from the steady state. The horizontal
axis measures time in quarters. . . . . . . . . . . . . . . . . . . . . . . 110
3.3.3.8 Relationship between expected investment and limited enforcement in
response to net worth shocks. . . . . . . . . . . . . . . . . . . . . . . . 111
3.6.2.1 Scatter: Standard Deviation of GDP and Contract Enforcement . . . . 126
7
Listings
A.1 Stata Do File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
A.2 Value Function Iteration . . . . . . . . . . . . . . . . . . . . . . . . . . 152
A.3 Simulation of Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
A.4 Main Program: Driver for Iteration and Simulation . . . . . . . . . . . 179
A.5 Grid Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
A.6 Model Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
A.7 Data Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
A.8 Array Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
A.9 Input Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
A.10 Matlab Codes for plots and statistics . . . . . . . . . . . . . . . . . . . 216
A.11 Matlab function for importing simulated data for plots . . . . . . . . . 226
A.12 Stata Do file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
A.13 Dynare code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
Word Count: 40,093
8
Abstract
The University of Manchester
Adams Sorekuong Yakubu Adama
Doctor of Philosophy (PhD) in Economics
Essays on Institutions, Firm Funding and SovereignDebt
24th October 2016
This thesis explores the effects of institutions on macroeconomic performance. Itdoes so in two main chapters, a summary of each of which is given below. In the firstmain chapter of the thesis, the interactions between government spending, governmentborrowing, political corruption and political turnover were examined. Incorporatingthese factors in a sovereign default model, we show how sovereign default decisions andbusiness cycle fluctuations are affected by the level of corruption. In particular, we showthat when there is turnover, corruption can generate higher risks of default and highercredit spreads when there is enough stability. Intuitively, we establish that a changein power from a less corrupt to a more corrupt government is more likely to causedefault than the reverse. The results also shows that households suffer welfare lossesas a result of corruption. As regards business cycles, the general effect of corruption isto alter business cycle statistics. Further, we estimate an empirical model using dataon sovereign default, corruption, political stability and other macroeconomic variablesfor a sample of emerging economies. The results of this provide strong evidence ofa positive relationship between both corruption and political stability and sovereigndefault.
The second main chapter of the thesis looks at the effects of limited financialcontract enforcement in a dynamic stochastic general equilibrium framework wherefirms have access to both internal and external means of finance. The results showshow limited enforceability affects fluctuations in key macroeconomic variables (e.g.,output, employment and price) through its impact on key financial variables (e.g.,interest rates, risk premium, default risk and leverage). In particular, we find thatweaker enforcement tends to amplify the effects of shocks, creating greater volatility,as well as lowering small firm funding. We provide some empirical evidence to supportour results. Using cross-country data on measures of financial market imperfections,we find that limited enforcement has a negative effect on output and that this effect isexacerbated by poor credit information. We also find that weaker contract enforcementis associated with higher output volatility.
9
Declaration
I, Adams Sorekuong Yakubu Adama, hereby declare that no portion of the work re-
ferred to in the thesis has been submitted in support of an application for another
degree or qualification of this or any other university or other institute of learning.
10
Copyright Statement
i. The author of this thesis (including any appendices and/or schedules to this
thesis) owns certain copyright or related rights in it (the “Copyright”) and he
has given The University of Manchester certain rights to use such Copyright,
including for administrative purposes.
ii. Copies of this thesis, either in full or in extracts and whether in hard or electronic
copy, may be made only in accordance with the Copyright, Designs and Patents
Act 1988 (as amended) and regulations issued under it or, where appropriate,
in accordance with licensing agreements which the University has from time to
time. This page must form part of any such copies made.
iii. The ownership of certain Copyright, patents, designs, trademarks and other in-
tellectual property ( the “Intellectual Property” ) and any reproductions of copy-
right works in the thesis, for example graphs and tables ( “Reproductions” ),
which may be described in this thesis, may not be owned by the author and may
be owned by third parties. Such Intellectual Property and Reproductions cannot
and must not be made available for use without the prior written permission of
the owner(s) of the relevant Intellectual Property and/or Reproductions.
iv. Further information on the conditions under which disclosure, publication and
commercialisation of this thesis, the Copyright and any Intellectual Property
and/or Reproductions described in it may take place is available in the Uni-
versity IP Policy (see http://www.documents.manchester.ac.uk/DocuInfo.aspx?-
DocID=487), in any relevant Thesis restriction declarations deposited in the
University Library, The University Library’s regulations (see http://www.man-
chester.ac.uk/library/aboutus/regulations ) and in The University’s policy on
Presentation of Theses.
11
Dedication
To the loving memory of my late God-father, Alhaji Abdul-Rahman Musah
a.k.a Mba Musah (Wilhem)
&
To the loving memory of my late father, Naa Adama Saaka.
12
Acknowledgments
Pursuing a doctoral degree in economics is a long and sometimes a tough journey. I
would first and foremost thank the Almighty God for His guidance throughout this
Ph.D journey. I would also like to thank all those who made this journey a joyful one.
In particular, I am greatly indebted to my supervisors, Professor Keith Blackburn, Dr.
Macnamara and Dr. Michele Berardi, for their constructive comments, suggestions,
support and guidance throughout my research. I would also like to thank them for
their time and energy spent reading through the draft copies of this thesis. I wish also
to thank the School of Social Sciences and the Economics Department for funding my
Ph.D programme.
I must also express my profound gratitude to all my friends at the Department
of Economics, the University of Manchester for all the insightful discussions we shared.
Special thanks go to Dr. Zeeshan Atiq and Dr. Johnson Gwatipedza for their invaluable
input and comments on the final draft of the thesis. I especially want to also thank
Dr. Abdilahi Ali for always being there for me whenever I needed him.
Indeed, many friends not from the Department of Economics, the University of
Manchester also contributed to the success of my Ph.D programme. Thanks go to
Dr. Justice Bawole, Dr. Hamza Bukari, Mr. Anthony Kumasey and Dr. Francis
Sanyare for their supports and inspirations during the challenging and great moments
we shared together as Ph.D candidates. I will also like to thank my neighbours at
Manchester; Sister Fatima Momori and her family, Mujeeb Iddrisu and his family, and
most especially Mr. Juda of Global African Limited for their support throughout my
Ph.D programme. I also say thank you to some important people in my life: Alhaji
Issifu Ali, Maulvi Gaffar and his family, Maulvi Bin Salih and his family, Mr. Nasir
Moomin, Mrs. Zainab Moomin, Hon. Godfred Bayon Tangu, Hon. Alhaji Adams
Mahama Issahaku (Okonkwo), Mr. Kassim Tangu Seidu, Mr. Theophilus Ofei Tetteh,
Mr. Adamu Jighi, Auntie Fati Seidu, Sister Ramatu Imoru Seidu, Mr. Simms Mensah
Kyei and his family, Dr. Samuel K. Annim and Dr. Pattick Asuming.
During my Ph.D programme, I had the opportunity to present my research (in-
cluding two of the chapters in this thesis) at international conferences including the
International the CSAE 26th Conference on Economic Development in Africa (Univer-
13
sity of Oxford), 2nd Annual International Interdisciplinary Conference on Challenges
to Development in Africa (Catholic University, Nairobi, Kenya), the Royal Economic
Society (RES) 2015 conference. I also presented my work in a number of seminars
at the University of Manchester, especially the Center for Growth and Business Cycle
Research (CGBCR) and Macroeconomics RAG seminar series. I wish to acknowledge
the suggestions, critics and comments I received from the participants.
Last but not the least, I would like to thank my lovely wife, Zulaiha Abdulai
Sorekuong-Adama, and my lovely son, Angsomwine Ramiz Sorekuong-Adama, for their
love and sacrifices.
I wish to pay tribute to my late father, Naa Adama Saaka and my God-father,
the late Alhaji Abdul-Rahman Musah a.k.a Mba Musah (Wilhelm) for being a great
source of inspiration to me. This thesis is dedicated to them.
And to everyone who has supported me either directly or indirectly, have my
heartfelt gratitude.
14
Chapter 1
Thesis Introduction
North (1989) defines institutions as “rules, enforcement characteristics of rules, and
norms of behaviour that structure repeated human interaction” (p.1321). In other con-
text, institutions are defined as humanly devised constraints that shape interaction
between people (see North (1990)). Fundamentally, in North’s view, the quality of
these institutions improves with limitations imposed on executive power. Generally,
institutional quality consists of certain key scopes such as voice and accountability,
political stability, rule of law, control of corruption, ease of doing business, regulatory
quality amongst others.
The importance of institutions in determining economic performance cannot be
underrated . By establishing clear and enforceable property rights, that minimise trans-
action costs and reduce the threat of coercion, good quality institutions can be decisive
in an economy’s prospects for growth and development. The importance of institutions
is well documented as is the diversity in institutional quality across different states (see
Knack and Keefer (1995); Rodrik et al. (2004); Hall and Jones (1999a)). Rodrik et al.
(2004) claim that good institutions is one of the most important factors to economic
development whilst Hall and Jones (1999a) find that cross-country differences in insti-
tutional quality are a major source of cross-country differences in capital accumulation,
productivity and per capita output.
The state is expected to provide the legal framework, infrastructure and stability
that is necessary for the creation of a favourable institutional environment. In many
15
instances, however, the state often fails in this role, leaving room for rent-seeking
activities (see Elliott (1997); Infante and Smirnova (2009); Treisman (2003); Ofer
(2003)). There is empirical evidence that rent-seeking is related (positively) to in-
stitutional weakness (see Mauro (1995); Acemoglu and Johnson (2004)). Interestingly,
rent-seeking could represent a mechanism that might improve economic performance
in the presence of weak institutions. This is the so-called “speed money” hypothesis,
according to which bribes paid to public officials may be a means of circumventing
cumbersome rules and regulations (red tape) that impede business efficiency. From a
different perspective, it has been argued that rent-seeking may be the necessary price to
pay for correcting institutional weaknesses. In other words, society may face a trade-off
between government failure and market failure (see Acemoglu and Verdier (1998, 2000);
Djankov et al. (2003); Acemoglu and Johnson (2004); Infante and Smirnova (2009)).
Acemoglu et al. (2003) in their study of the effect of institutions on macroeconomic
policies observed that there are deeper institutional causes of economic instability and
poor macroeconomic performance, such as law and order.
One manifestation of weak institutions is corruption. Though there is no one
acceptable definition of corruption, Transparency International, generally, defines cor-
ruption as the abuse of entrusted power for private gain, by especially public sector
officials. Public sector corruption is defined by Blackburn et al. (2006) as “the abuse of
authority by bureaucratic officials who exploit their powers of discretion, delegated to
them by the government, to further their own interests by engaging in illegal, or unau-
thorised, rent-seeking activities” (p.2448). It is in this light that the World Bank1 ar-
gues that corruption is “the single greatest obstacle to economic and social development.
It undermines development by distorting the rule of law and weakening the institutional
foundation on which economic growth depends”. The relationship between corruption
and other macroeconomic variables has been studied extensively in the literature (see
Mauro (1995); Knack and Keefer (1995); Li et al. (2000); Dreher and Herzfeld (2005)).
Mauro (1995) conducts an empirical investigation into the relationship between corrup-
1http://www.worldbank.org/
16
tion and economic growth, concluding that corruption has a significant negative impact
on investment. Knack and Keefer (1995) and Li et al. (2000) find similar results, as do
Dreher and Herzfeld (2005) who calculated that an increase in International Country
Risk Guide (ICRG) index of corruption by one point reduces growth by 0.13% points
and GDP per capita by US$ 425. Corruption can also have distributional effects, with
several studies identifying a positive correlation between the level of corruption and
the degree of income inequality (see Li et al. (2000)).
One of the major channels through which corruption can affect growth is its im-
pact on public policy. There are many ways in which this might occur, some more direct
than others. On one side of the government’s balance sheet, corruption can cause a
misallocation of public expenditures away from growth-promoting areas (such as edu-
cation and health) towards bribe-generating areas (such as military and defence) (see
Gupta et al. (2001); Mauro (1998); Tanzi and Davoodi (1997)). For the same reason,
expenditures may be misallocated away from the most to the least cost-effective means
of public procurement, producing inefficient and inflated levels of spending (see Black-
burn et al. (2011)). On the other side of the balance sheet, corruption can lead to a
loss of tax revenues and other public funds, as evidenced in a number of studies (see
Tanzi and Davoodi (2000, 1997); Ghura (1998); Imam and Jacobs (2014)). This may
compromise the delivery of pro-growth social programmes and, in doing so, weaken in-
dividuals’ incentives to save and invest (see Blackburn and Sarmah (2008)). It may also
force the government to raise taxes or to seek additional means of distortionary finance,
including inflationary finance (see Al-Marhubi (2000); Blackburn and Powell (2011b)).
In a different vein, corruption in regulation can cause a dilution of property rights and
an escalation of the costs of doing business, each of which may impede innovation and
entrepreneurship (see Hall and Jones (1999b); North (1990); Sarte (2000)).
Beyond public policy, there are other ways in which corruption can affect eco-
nomic performance. One of these is by inducing a misallocation of talent away from
productive (entrepreneurial) activities towards non-productive (rent-seeking) activities
(see Ehrlich and Lui (1999); Murphy et al. (1991)). Another is by imposing deadweight
17
losses on society through the costs of trying to conceal and expose corrupt behaviour
(see Blackburn et al. (2006); Blackburn and Forgues-Puccio (2007)).
Corruption can affect other macroeconomic variables and other aspects of mac-
roeconomic policy. Of particular interest to this thesis is the effect of corruption on
government finance especially when the government relies heavily on borrowing. Cor-
rupt public officials may confiscate loaned funds or block other sources of government
income, thereby limiting the government’s ability to meet its debt obligation. For in-
stance in Russia more than US$4 billion in IMF loans was believed to have disappeared
shortly before Russia’s default in 1998 (see Ciocchini et al. (2003)). Work by Haque
and Sahay (1996), Tanzi and Davoodi (1997), and Johnson et al. (1999) shows that
higher levels of corruption are associated with lower tax revenue, which could other-
wise be used by the government to repay its debt. Ciocchini et al. (2003) investigate
the effect of corruption on sovereign bond spreads, observing that higher levels of cor-
ruption are associated with higher spreads. The same authors observe that corrupt
governments require high liquidity which induces them to borrow even under very high
spreads. Transparency International reported that corruption was one of the triggers
of the Greek2 debt crisis (see Corruption triggered Greek Debt Crisis-Transparency
International).
Another issue that is particularly relevant to this thesis is the effect of institutional
weaknesses on the functioning of financial markets. Good legal institutions (rule of law
in the form of quality of property rights, contract enforcement, the police, and the
courts etc.) are generally argued to be essential for fostering financial development.
Such institutions play a vital role in protecting investors through the enforcement of
property rights and contractual arrangements. This creates room for risk sharing and
a willingness of investors to supply funds to firms (see La Porta et al. (1997); Lopez de
Silanes et al. (1998); La Porta et al. (2000)). Albuquerque and Hopenhayn (2000)
argue that better enforcement of contracts has serious implication for the funding of
small firms and growth. Yet, the inability of these legal institutions to enforce financial
2http://www.spiegel.de/international/europe/european-debt-crisis-greek-corruption-booming-says-transparency-international-a-681184.html
18
contracts is what we refer to as weak (limited or imperfect) contract enforcement. That
is to say, limited contract enforcement is the difficulty with which lenders can recover
defaulted loans. Others, including the World Bank, have likened (limited) contract
enforcement to the time and cost for resolving commercial dispute through courts–cost
of contract enforcement.
In light of the foregoing discussion, this thesis is broadly concerned with the rela-
tionship between institutional quality, government debt and firm funding together with
the implications of this for macroeconomic outcomes. The thesis seeks to contribute to
the (theoretical) literature on sovereign default by studying specifically the influence
of corruption and political turnover on sovereign default decisions. It does so within
the context of a Dynamic Stochastic General Equilibrium (DSGE) model which allows
for the random political turnover of alternative types of government that have differ-
ent propensities to be corrupt. We contribute to the empirical literature of sovereign
default by analysing the influence that corruption and political factors could exert on
sovereign default risk. We distinguish between corruption and political stability (which
is not done in the literature (see Chapter (2) for details) in order to investigate the
influence that each independently exerts on sovereign default. We contribute to lit-
erature on financial development by studying the upshot of limited financial contract
enforcement (institutions) on financial markets and macroeconomic outcomes. Spe-
cifically, our first line of contribution is to the literature on agency costs, asymmetric
information and financial development where we study the role of limited contract en-
forcement in a Dynamic Stochastic General Equilibrium (DSGE) framework. We do
so by allowing for the possibility of the firm being able to default on bank loans when
it is still solvent, though a defaulting firm faces the prospect of being punished if it
is caught. Empirically, we contribute to the literature on macroeconomic performance
and financial development by using data that has current trends covers a wide range of
countries. The thesis consists of two main essays; a summary of which is given below.
In the first essay we study sovereign borrowing and sovereign default risk in a
dynamic general equilibrium model of corruption and political turnover. Many govern-
19
ments across the world borrow to finance their budget deficits. An obvious question
is why do some governments borrow more than others and why do some governments
default more than others? Evidence suggests that weak institutions in the form of
corruption may be the answer. We provide an explanation for this by demonstrating
how corruption (modelled as the embezzlement of public funds) may influence sover-
eign borrowing and default decisions on the part of alternating incumbent governments
with different propensities to be corrupt. We show that when there is turnover between
governments with different governments, corruption can generate high default risk and
high credit spreads, but only when there is enough stability. We establish that a change
in power from a less corrupt to a more corrupt government is more likely to increase this
default risk than the reverse. We also find that welfare loss to households is increasing
with the level of corruption. As motivation and support for our analysis, we present
some empirical evidence to show that corruption is, indeed, associated with higher risks
of default. The empirical evidence also shows a strong positive relationship between
political stability and risks of default.
In the second essay we study financial intermediation and firm financing in a
dynamic general equilibrium model of capital market imperfections resulting from in-
stitutional weaknesses. The legal enforcement of contracts plays an important role
when contractual issues cannot be solved amicably between lenders and borrowers es-
pecially in emerging economies. Yet the legal institutions required for this are often
very weak or non-existent implying that contract enforcement is limited. We explore
the implications of this by considering the effect of poor quality institutions (imperfect
contract enforcement) on firms’ financial arrangements with lenders, firms’ decisions
to default and firms’ access to working capital.
We establish a pro-cyclical risk premium following a positive aggregate productiv-
ity shock. However, we find that a shock to net worth in the form of one-time wealth
transfer from entrepreneurs to households results in a counter-cyclical risk premium.
This transfer reduces entrepreneurial net worth and causes a fall in the supply of cap-
ital which then pushes up the price of capital. The fall in net worth also results in
20
increasing demand for external finance which in turn causes a rise in the probability of
default and the lending rate. The risk premium depends on the probability of default,
the price of capital, the lending rate and and the strength of contract enforcement.
Overall, the lending rate, the risk premium and the default probability are increasing
in the degree of limited contract enforcement. This risk premium provides the key
mechanism through which the effects of shocks are amplified by limited contract en-
forcement; the latter which also results in greater output volatility. Consequently, high
degree of limited contract enforcement imposes a negative effect (in the form of high
lending rate) on small firms (which are forced to rely more on external finance) seeking
to borrow in order to finance investment. This is particularly onerous for smaller firms,
the growth of which is therefore impeded. As motivation and support for our analysis,
we present some empirical evidence which shows that a weaker enforcement (or higher
cost of enforcement) of financial contracts is associated with a lower level, lower growth
rate and higher volatility of output.
The rest of the thesis is organised as follows. In Chapter (2), we investigate
the influence that corruption and political turnover (risk) have on sovereign default
decisions. We study the effect of limited financial contract enforcement on macroe-
conomic outcomes in Chapter (3). In Chapter (4), we present the conclusion of the
thesis, also highlighting its limitations and directions for further research.
21
Chapter 2
Corruption and Political Turnover
in a Sovereign Default Model
2.1 Introduction
Business cycles in emerging economies vary from their developed counterparts. Such
economies are typically characterised by relatively high interest rates and interest rate
spreads, high output volatility, low output per capita, weak institutions, high levels of
corruption, high political instability and high frequencies of sovereign default. The last
of these phenomena (like most of the others) has attracted the attention of academics
and policymakers for a long time, and a renewed interest has been ignited by recent
events in the world. This chapter of the thesis seeks to contribute to the literature on
sovereign default by studying specifically the role of corruption in influencing default
decisions. It does so within the context of a Dynamic Stochastic General Equilibrium
(DSGE) model which allows for the random political turnover of alternative types
of government that have different propensities to be corrupt. Corruption manifests
itself as the embezzlement of public funds. Specifically, public sector corruption is
defined as “the abuse of authority by bureaucratic officials who exploit their powers
of discretion, delegated to them by the government, to further their own interests by
engaging in illegal, or unauthorised, rent-seeking activities” (Blackburn et al. 2006,
p.2448). The results of the analysis highlight the important role that corruption can
22
play in determining the risk of default, a role that is evidenced by the data.
Sovereign default has been attributed to various causes, both economic and polit-
ical. In their seminal work, Hatchondo et al. (2009) introduce political factors into the
modelling of sovereign default which they claim to have accounted for defaults in Brazil
during 2002 and Argentina during 2001. The authors present a model with political
turnover, where different government types are distinguished in terms of their degree of
impatience which influences their willingness to pay off debt. In turn, this affects the
equilibrium bond spread through a direct impact on each type’s borrowing opportunit-
ies. It is shown that sovereign default may be triggered when the government changes
from a more patient to a less patient type, provided that there is enough political
stability. This suggests that political turnover may have significant implications for
sovereign default decisions. The model also illustrates a non-monotonic relationship
between political stability and default probability which is in line with the political
turnover models of Amador (2003) and Cuadra and Sapriza (2008), where political
stability affects sovereign bond spreads through future utility flows. Though default
episodes have mostly occurred in periods of downturns, there is, nevertheless, evidence
that a considerable number of default episodes occur when output is above its long-run
trend (see Tomz and Wright (2007); Hatchondo et al. (2009)).
The foregoing analyses yield important insights, though one issue that is not ad-
dressed, but which merits attention, is the role of corruption in influencing the risk of
sovereign default. This is particularly pertinent for emerging economies, and there are
good reasons for thinking why corruption may be important for default decisions. For
instance, a corrupt policymaker may be willing to borrow substantial funds even with
high interest rate spreads in order to create opportunities for appropriating resources.
As a result, corruption may lead to a higher incidence of default if loan repayments
become excessive. Ciocchini et al. (2003) studied the effect of corruption on sovereign
bond spreads in emerging economies and observed that high levels of corruption are
associated with high spreads. Importantly, the authors argue that corrupt governments
need liquidity which results in high borrowing even with very high spreads. Further-
23
more, if corruption leads to a drain on loaned funds and other sources of government
income, then it may limit the government’s ability to meet its debt obligations. For
instance, in Russia more than $4 billion in IMF loans apparently disappeared shortly
before Russia’s default in 1998 (see Ciocchini et al. (2003)). Similarly, Haque and Sahay
(1996), Tanzi and Davoodi (1997), and Johnson et al. (1998) observe that higher levels
of corruption are associated with lower tax revenues, which would in turn lower the
government’s ability to repay its debt. One observation is that most of the countries
that default seem to be the most corrupt. In addition, the data suggests that there is
a strong correlation between sovereign default, corruption and political turnover.
In spite of the above, little or no attempt has been made to explore the inter-
linkages between corruption and the risk of default. This paper seeks to do so. The
analysis is based on a DSGE model in which different government types alternate in
power. Corruption takes the form of a government’s illegal consumption of public
funds, which impacts on the decision to default. The government borrows in order to
smooth household consumption, although it is only partially benevolent in this respect
due to its proclivity towards corruption. A government may be either of two types–a
more corrupt or a less corrupt type–which alternate in power with a certain probab-
ility. The government in office makes a decision about whether or not to default by
trading off the benefits and costs associated with this. The benefits of defaulting are
the avoidance of debt repayments, whilst costs are a loss of output in the following
period. We show how default decisions, together with business cycle fluctuations, are
affected by the level of corruption. We find that more corrupt governments are more
likely to default, conditional on the same endowment and initial debt. Moreover, the
presence of political turnover makes it possible for corruption to generate high default
risk and high credit spreads, but only when there is enough political stability. With
turnover, the less corrupt government pays a premium to lenders to compensate them
for the possibility that the more corrupt government will come into power next period
and default. When there is a lot of instability, the less corrupt government avoids
increasing debt levels to the point where the corrupt government would default, result-
24
ing in lower credit spreads. However, when there is enough stability, the less corrupt
government is willing to borrow at levels which the more corrupt government would
default. While the probability that the high type comes into power is low, this still
results in higher default risk and higher credit spreads. We also compute the welfare
loss to households as a result of corruption and show that this loss is increasing with
the level of corruption.
To set the scene for our theoretical analysis, we first conduct an empirical invest-
igation into the determinants of sovereign default. Using data on a broad sample of
emerging economies, we find that, amongst other factors, both corruption and political
stability have a significant positive influence on sovereign default.
2.1.1 Related Literature
2.1.1.1 Theoretical literature
This paper is closely related to the models of Cole et al. (1995), Alfaro and Kanczuk
(2005), and Hatchondo et al. (2009). These models study sovereign default with het-
erogeneous borrowers where a patient policymaker is replaced by an impatient poli-
cymaker. Cole et al. (1995) and Alfaro and Kanczuk (2005) focus on equilibria in
which patient policymakers never default and impatient policymakers always default.
Hatchondo et al. (2009) consider a political process similar to the one used by Cole
et al. (1995), and Alfaro and Kanczuk (2005), but differ in the government’s choice of
optimal borrowing level and in both policymakers being able to default. They show
that if there is enough political stability and a patient government also encounters poor
economic condition, a default is likely to be triggered by political turnover. In addi-
tion, they find that the presence of political turnover can result in an increase in the
volatility of the spread paid by patient governments in politically stable economies. We
study sovereign default in an environment similar to that of Hatchondo et al. (2009)
and find that the presence of political turnover results in an increase in the volatility
of spread paid by both types of governments and this increase is greater with the more
corrupt type.
25
Information on borrower types to lenders in the literature is mixed. Many recent
models of sovereign default with heterogeneous borrowers assume that lenders cannot
directly observe a borrower’s type (see Chatterjee et al. (2007)). Hatchondo et al.
(2009), on the contrary, assume that the type of policymaker in power is public in-
formation to lenders. Hatchondo et al. (2009) also allow policymakers to choose debt
levels from a continuum. We make similar assumptions as Hatchondo et al. (2009).
A number of models (see Cole et al. (1995); Alfaro and Kanczuk (2005)) assume
representation of borrowers with stochastic preferences where borrower types change
over time. Hatchondo et al. (2009), on the other hand, assume a representation of
political processes, similar to Amador (2003), and Cuadra and Sapriza (2008) but
where borrowers of different types alternate in power. Amador (2003), and Cuadra and
Sapriza (2008) in their setup assume that types only differ on the optimal allocation
of resources within each period and receive the same treatment from lenders. They
also assume that political stability affects the equilibrium spread mainly through its
impact on the weight of future utility flows. On the contrary, Hatchondo et al. (2009)
in their setup assume that the two types differ in their willingness to pay. They
equally argue that political stability affects equilibrium spreads mainly through the
direct effect it puts on the borrowing opportunities of a government. In our setup, the
two types differ in their willingness to pay and the risk of being replaced, the latter
effect exacerbated by the propensity of a type to be corrupt. We focus on a single
discount factor case, whilst the other models (see Amador (2003); Cuadra and Sapriza
(2008); Hatchondo et al. (2009)) consider different discount factors as a representation
of types. In our setup, types are represented by their propensity to be corrupt. We
argue that political stability, which is aggravated by how corrupt a type is, affects
equilibrium spreads through its impact on the policymaker’s borrowing opportunities
and how lenders perceive types.
Earlier studies (see Aguiar and Gopinath (2006); Chatterjee et al. (2007)) have
used shocks to endowment growth rate and shocks to borrower’s discount factor as
tools to smooth out the equilibrium bond price function faced by the borrower and as a
26
mechanism in generating a higher spread and higher spread volatility. The introduction
of political turnover in the Hatchondo et al. (2009) model serves as the mechanism
through which smoother bond price functions are delivered. In our setup, building on
Hatchondo et al. (2009), political turnover impacts on the bond price function and also
amplifies the effect of corruption in the model.
2.1.1.2 Empirical literature
The empirical literature on the determinants of debt crisis is broad (see Schimmelp-
fennig et al. (2003); Lausev et al. (2011)). Earlier studies (see Frank and Cline (1971))
have made findings on the possibility of predicting debt crisis. On the contrary, other
studies (see McFadden et al. (1985)) have found that predicting debt crises might be
difficult. McFadden et al. (1985) in their study on finding probabilities of debt crisis
using data for 93 countries over the period 1970-1982, conclude that predicting debt
crises in advance might be difficult even though an econometric model can help to
explain sovereign debt problems. To this effect, they find debt burden, the level of per
capita income and real GDP growth, to mention few, as significant predictors of debt
crisis.
Commonly included in the econometric models are short-term financial variables
like debt-GDP ratio and long term variables like GDP growth. Specifically, Schimmelp-
fennig et al. (2003) as cited in Lausev et al. (2011) find high external debt to GDP ratio
and short term debt to be highly associated with debt rescheduling. Detragiache and
Spilimbergo (2001a) find the importance of liquidity factors such as short-term debt,
debt service, and the level of international reserves as determinants of debt crises. They
do not only identify countries that are more open as in a better position to service their
debt, but find inverse relationship between liquidity of a country and the probability
of default. Edwards (1984), Min (1998), and Rowland and Torres (2004) recognise the
importance of various macroeconomic variables in determining credit spreads.
Besides economic variables, political risk and institutional variables have often
27
been considered to play an important role in predicting sovereign debt crises among
emerging market countries. Balkan (1992), one of the earliest attempted studies on this
issue, finds an inverse relationship between probability of rescheduling and the level of
democracy for a country, on the one hand, and a direct relationship between probab-
ility of rescheduling and political instability, on the other hand. Furthermore, Verma
(2002) finds that more democratic countries tend to default more, whilst Bordo and
Oosterlinck (2005) observe that half of the default incidents during 1880-1913 occurred
around periods of political turnovers. Citron and Nickelsburg (1987) and more recently
Georgievska et al. (2008) uphold the importance of political factors in determining debt
rescheduling probabilities. According to Baldacci et al. (2011), higher political risk is
also associated with higher spreads. A number of recent studies have also stressed the
significance of such political variables in determining sovereign default and debt res-
cheduling (see Ul Haque et al. (1998); Reinhart et al. (2003); Santiso (2003); Van Rijck-
eghem and Weder (2004); Sturzenegger and Zettelmeyer (2006); Moser (2007); and
Lausev et al. (2011)).
Kraay and Nehru (2006), one of the earliest attempted studies on debt crisis and
institutions, find the quality of institutions and policies to have major effect on debt
rescheduling. Similarly, Butler and Fauver (2006) identify the quality of a country’s
legal and political institutions as having a major role play in determining sovereign
credit ratings. In addition, Ciocchini et al. (2003) study the effect of corruption on
sovereign bond spreads in emerging economies and observe that high levels of corruption
are associated with high spreads.
The impact of past debt repayment records on current and future rescheduling
have been investigated in a number of studies. Specifically, McFadden et al. (1985),
Li (1992), Aylward and Thorne (1998), and most recently Lausev et al. (2011) have
found debt repayment history as a strong determinant of future debt crisis.
We contribute to the empirical literature by analysing the influence that corrup-
tion and political factors could exert on sovereign default risk. We distinguish between
corruption and political stability (which is not done in the literature (see Balkan (1992);
28
Li (1992); Verma (2002); Bordo and Oosterlinck (2005) and Lausev et al. (2011)) in
order to investigate the influence that each independently exerts on sovereign default.
We find a result that is puzzling. Using data on a broad sample of emerging economies
over the period 1984-2008, we find that, amongst other factors, both corruption and
political stability have a significant positive effect on sovereign default. We contribute
to the theoretical literature by studying how corruption together with political turnover
can affect sovereign default decision in a dynamic general equilibrium setting. The rest
of the paper is organised as follows. In Section (2.2), we present the empirical analysis
of the determinants of sovereign default. In Section (2.3), we set out the theoretical
model that we use to study the relationship between sovereign default and corruption.
The theoretical model is intended to find solution to the problems, such as endogeneity,
that our empirical model might run into. In Section (2.3.2), we solve the model. In
Section (2.4), we calibrate the model and present our main results. In Section (2.5),
we make some concluding remarks.
2.2 Empirical Observations
This section looks empirically at the influence that corruption and political factors have
on sovereign default. Our main objective is to evaluate the extent to which corruption
and political factors have direct or indirect effects on the risk of default. Taken together,
our results suggest that there is a significant positive association between sovereign
default and both corruption and political stability, controlling for other important
determinants of default. This central finding remain fairly robust to a battery of
sensitivity analyses, including alternative specifications.
2.2.1 Data Sample
We use annual data on sovereign default and rescheduling episodes and possible predict-
ors of sovereign default and rescheduling over the period 1984-2008. Our own empirical
investigation is based on data from the World Bank Development Indicators, World
Bank–Global Development Finance (1991, 2006, 2012), Standard and Poors, Moodys
29
and the International Country Risk Guide by the Political Risk Services (PRS). We
consider the following variables as potential predictors of sovereign default: corruption,
political stability and various controls such as external debt, annual GDP growth and
logarithm of GDP Per Capita. We focus on emerging economies, where the selection
of countries is based on the availability of data and also controlling for outliers. Vari-
ables used in the estimation and the summary statistics are detailed in Table (2.7.1.2)
and Table (2.7.1.3), respectively. Among these variables, GDP per Capita is the most
volatile followed by political stability and then corruption. That is volatility of 2.411,
1.891 and 1.039, respectively.
2.2.1.1 Dependent Variable
Existing studies on sovereign debt crisis show that there is no laid down definition of a
sovereign debt crisis, a sovereign default episode, or a sovereign debt rescheduling event
(see for example Kraay and Nehru (2006); Schimmelpfennig et al. (2003); Lausev et al.
(2011) and Ciarlone and Trebeschi (2005)). Generally, sovereign default or sovereign
debt rescheduling is any failure by a nation to meet its debt obligations. This may
involve either missing a scheduled payment of principal or interest. Specifically, the
IMF and the World Bank have considered rescheduling agreements on external debt
as sovereign defaults. In our context the dependent variable is sovereign default. We
consider a country as having defaulted if there was an outright default of debt or if
there was reported reschedule of the principal or interest, as is reported in Standard and
Poors, Moodys, World Bank Development Indicators, the IMF and World Bank–Global
Development Finance (1991, 2006, 2012). Using this data, we establish the following
criterion for determining the dependent variable (default): A default is registered if a
country defaults or reschedules its debt or the interest on its debt in a given year. As
argued in the literature rescheduling could be inability on the part of the borrower to
settle the terms of the contract and can be treated as a proxy for default. We look at
sovereign default episodes for emerging economies over the period 1984-2008. We use
30
25 countries after controlling for outliers as displayed in Table (2.7.1.1).
2.2.1.2 Independent Variables
We undertake our analysis using macroeconomic variables, otherwise known as solvency
variables, as controls and institutional variables that normally explain a country’s
sovereign debt rescheduling or default risk. These variables can be put into the following
categories: (a) institutional variables, (b) macroeconomic/solvency variables, (c) past
variables (past default record, past of institutional variables and past macroeconomic
variables).
(a) Institutional Variables
(i) Corruption
Corruption has been identified as a major political risk factor (see Political Risk Services
(PRS1)). This risk in corruption results from the fact that at some point in time some
major scandal could be revealed, which has the propensity to provoke tension and cause
a fall or overthrow of the government. This could further bring about a readjustment in
the country’s political institutions, a breakdown in law and order, making the country
unstable and ungovernable (see PRS). In an assessment of corruption, PRS (2008)
has identified “financial corruption in the form of demands for special payments and
bribes connected with import and export licenses, exchange controls, tax assessments,
police protection, or loans” (p.31) as the most common form of corruption encountered
by business. We use the International Country Risk Guide Index (ICRG) measure of
corruption by PRS which uses a scale of 0-6 (6 is the highest rank of transparency)
that we convert to 0-6 (to capture the level of corruption than transparency), where 6
is the highest rank of corruption.
1http://www.prsgroup.com/
31
The (Un)reliability of Measures of Corruption
Corruption data has been used widely in empirical studies. Nevertheless, the reliabil-
ity of it measurement still remains an issue in empirical studies. A reliable measure of
corruption should be one that objectively quantifies the frequency and the magnitude
of corruption over time and across countries, which is often impossible (see Swaleheen
(2011)). However, as a result of the lack of objective measure of corruption, current
empirical studies on corruption mostly use subjective measures by Transparency In-
ternational (TI), the World Bank (WB) and Political Risk Services (PRS). Whilst the
TI and WB measures of corruption are composite indices based on individual surveys
of corruption, the PRS measure is an expert rankings by a specialised institution. It
measures corruption that exists within the political system which has the ability to
affect foreign investment through distortion in the economic, financial and business en-
vironment. Among the subjective measures available, the ICRG measure of corruption
by PRS is widely accepted as being reflective of the frequency and magnitude of cor-
ruption. Data for this measure is available from 1984. Also due to its broad coverage
of countries, it has had wide usage (see Knack and Keefer (1995); Braun and Di Tella
(2004); Dreher and Siemens (2003); Dal Bo and Rossi (2007); Swaleheen (2011) and
Lausev et al. (2011)).
(ii) Political Stability
In our attempt to examine the effect of political turnover on sovereign default risk,
we use the Political Rights Index (PR) from Freedom House as a measure of political
stability. This measure has been used by Verma (2002) as a proxy for democracy
which the author argues is sometimes equated with political stability. The PR is
measured on a scale of 1-7 which we convert to 0-10, where 10 represents the best rating
of political rights. Freedom House (https://freedomhouse.org) recognises that “Free
elections provide long-term political stability and allow citizens to peacefully replace
ineffective or corrupt leaders. And independent media provide a check on government,
32
verifying official claims of success and exposing abusive practices”. It is in the light
of this that we use the Political Rights Index as a proxy for political stability in our
work.
It must be pointed out that the measures of corruption and political stability,
especially the ICRG measures, do not include sovereign default risk (the dependent
variable) in country ratings. By this, we avoid a possible double counting problem
that would result from having the dependent variable regressed on a variable that
include itself.
(b) Macroeconomic/Solvency Variables
Several macroeconomic variables which may predict sovereign default are used as con-
trols in our estimation. Included amongst these are external debt-GDP ratio, logarithm
of GDP per Capita and the annual growth rate of GDP. Data on all of these are taken
from the World Development Indicators (WDI).
GDP growth rate which captures the current economic performance of a country
has been argued to have a negative impact on the probability of default (see Lausev
et al. (2011)). Similarly, GDP per Capita which captures the level of development
of a country has been argued in the literature to have a negative relationship with
the sovereign default probability (see Feder and Just (1977) as cited in Lausev et al.
(2011)). In related studies (see Williams (2014)), GDP per Capita and growth of
GDP per Capital have both been used to control for differences in financial system
development and economic cycle effects. It is also argued that a country that increases
its external debt in relation to its GDP is likely to have unsustainable debt which could
in turn increase the probability of default. Accordingly, a positive relationship between
external debt-GDP ratio and the probability of default is expected.
33
(c) Past Default/Rescheduling Records and Past of Current Explanatory Variables
Previous studies on sovereign debt have found evidence of past debt repayment records
having positive effect on future default (see McFadden et al. (1985); Aylward and
Thorne (1998); Li (1992) and Lausev et al. (2011) etc.). Following these findings,
we include past default record as an explanatory variable. Similarly, the inclusion of
the past of explanatory variables is to capture the impact of the previous state of the
economy on the current one (see McFadden et al. (1985); Balkan (1992) and Pestova
(2015)). McFadden et al. (1985) argue that the reason for the inclusion of the lagged
explanatory variables is to reduce the problem of simultaneity.
2.2.2 Model Specification
A probit model is used to test the correlations of the macroeconomic and political
predictor variables with default of debtor country. Our empirical specification amongst
other is in line with Rahnama-Moghadam (1995) and Balkan (1992). To define a probit
model, consider a country i observed over T periods of time t, where t = 1, ..., T and
i = 1, ..., N . We think of an unobservable random variable, y∗it, as the underlying latent
propensity that an observable binary outcome, yit, will be such that
yit =
1 if y∗it > 0
0 otherwise
Since we are interested in default occurrence rather than the amount of debt defaulted,
the dependent variable (default) is a discrete random variable that takes the value 0 if
a country does not default during a given year and 1 if it does.
In our setting, the independent variables may be either continuous or discrete.
The dependent variable y∗it is a function of explanatory variable(s) xit, a constant α and
random error term uit. The probit model used to test our prediction is summarised as:
34
y∗it = α +m∑j=1
βjxjit + uit (2.2.2.1)
where yit = 1 if country i has rescheduled or defaulted on its debt payments in year
t and 0 if otherwise, and xjit is the jth macroeconomic or political variable of country
i in year t. We interpret the coefficients β1, β2..., βm as the partial derivatives of the
probability of default with respect to the independent variables, x1i, x2i..., xmi. In this
light, given the macroeconomic or political characteristics, x1i, x2i..., xmi, the binary
response model determines the probability that country i will default or reschedule its
debt, against the alternative that country i will not. We estimate the model in Stata
and code is provided in Appendix (A.1).
2.2.3 Results
The central argument of this paper is that there is a significant relationship between
corruption, political risk and sovereign default risk. The analysis will centre on the
variables of interest (corruption and political variables). We first report the results
(with the marginal effects) of our baseline probit model where we regress default on
current explanatory variables. Table (2.7.1.4) reports these findings. Column 1 of Table
(2.7.1.4) shows our results when we include external debt-GDP ratio and real GDP
growth as control variables. The coefficient on corruption has the expected positive sign
and insignificant. The coefficient on political stability is significant at 5%. Using the
corresponding marginal effect in column 4 of Table (2.7.1.4), the estimated probability
effects of corruption and political stability are 0.028 and 0.025, insignificant at 10%
and significant at 5%, respectively. This implies that a unit change in corruption will
increase the probability of default by 3%, similarly a unit change in political stability
will increase the probability of default by 3%. The model specification in column
2 of Table (2.7.1.4) shows our result when we include external debt-GDP ratio and
GDP per Capita as control variables. The coefficient on corruption has the expected
positive sign and significant at 10% whilst the coefficient on political stability is positive
35
and significant at 5%. Using the corresponding marginal effect in column 5 of Table
(2.7.1.4), the estimated probability effects of corruption and political stability are 0.036
and 0.025, significant at 10% and 5%, respectively. This implies that a unit change
in corruption will increase the probability of default by 4%, similarly a unit change in
political stability will increase the probability of default by 3%. The model specification
in column 3 of Table (2.7.1.4) shows our results when we include external debt-GDP
ratio, real GDP growth and GDP per Capita as control variables. The coefficient on
corruption has the expected positive sign and significant at 10% whilst the coefficient
on political stability is positive and significant at 5%. Using the corresponding marginal
effect in column 6 of Table (2.7.1.4), the estimated probability effects of corruption and
political stability are 0.036 and 0.025, significant at 10% and 5%, respectively. This
implies that a unit change in corruption will increase the probability of default by 4%,
similarly a unit change in political stability will increase the probability of default by
3%.
The existing empirical literature (see Balkan (1992); Li (1992); Verma (2002);
Bordo and Oosterlinck (2005) and Lausev et al. (2011)) on sovereign default and polit-
ical risks do not distinguish between corruption and political (in)stability. We distin-
guish between the two in order to investigate the influence that each (corruption and
political stability) independently exerts on sovereign default. We find a result that
may seem puzzling. We find that the coefficient on corruption is positive in all cases
which continues to indicate that higher corruption is associated with a higher sovereign
default probability. Also, we observe a positive coefficient for political stability in all
cases. It would be generally thought that political instability is conducive to sovereign
default but our results indicate otherwise. The reason for the positive effect of polit-
ical stability on default risk lies in its ability to create room for more borrowing. We
therefore argue that the positive sign is consistent with findings in the literature (see
Verma (2002); Bordo and Oosterlinck (2005)) that suggest that political stability or
democracy has positive influence on sovereign default. Also, the findings from our the-
oretical model show that higher political stability increases default probability because
36
the former creates an enabling environment for more borrowing, a mechanism similar
to Hatchondo et al. (2009).
2.2.3.1 Robustness Analyses
We test the sensitivity of our baseline results to other specifications of the model. In
particular, we check for robustness by specifying the model with lagged explanatory
variables and by including lagged dependent variable as an explanatory variable. As
we have argued earlier these specifications with lagged explanatory variables (including
lagged dependent variable) is supported by the literature (see McFadden et al. (1985);
Balkan (1992); Li (1992); Aylward and Thorne (1998); Lausev et al. (2011) and Pestova
(2015)).
Our first check for robustness involves running a probit model of current default
on past explanatory variables. Table (2.7.1.5) reports our findings. Column 1 of Table
(2.7.1.5) shows our result where we include past external debt-GDP ratio and past real
GDP growth as control variables. The result shows that the coefficient on corruption
is positive and significant at 10%. The general conclusion to be drawn is that higher
levels of corruption are associated with greater risks of sovereign default, as our baseline
results suggest. The coefficients on political stability is positive, significant at 1% and
consistent with our baseline results. Using the corresponding marginal effect in column
4 of Table (2.7.1.5), the estimated probability effects of corruption and political stability
are 0.036 and 0.030, significant at 10% and 1%, respectively. This implies that a unit
change in corruption will increase the probability of default by 4%, similarly a unit
change in political stability will increase the probability of default by 3%. In column
2 of Table (2.7.1.5) is our result when we include past external debt-GDP ratio and
past GDP per Capita as control variables. The result shows that the coefficient on
corruption is positive and significant at 10% whilst the coefficient on political stability
is positive, significant at 1% and consistent with our baseline results. By including
past GDP per Capita as a control variable, the effect of past corruption on default is
37
bigger than when we include past real GDP growth as a control variable. Using the
corresponding marginal effect column in 5 of Table (2.7.1.5), the estimated probability
effects of corruption and political stability are 0.040 and 0.029, significant at 10%
and 1%, respectively. This implies that a unit change in corruption will increase the
probability of default by 4%, similarly a unit change in political stability will increase
the probability of default by 3%. The result in column 3 of Table (2.7.1.5) displays
our findings where we include past external debt-GDP ratio, past real GDP growth
and past GDP per Capita as control variables. The result shows that the coefficient on
corruption is positive and significant at 5% whilst the coefficient on political stability
is positive, significant at 1%. As we include both past real GDP growth and GDP
per Capita as a control variables, the effect of past corruption on default increases.
Using the corresponding marginal effect column in 6 of Table (2.7.1.5), the estimated
probability effects of corruption and political stability are 0.043 and 0.029, significant at
5% and 1%, respectively. This implies that a unit change in corruption will increase the
probability of default by 4%, similarly a unit change in political stability will increase
the probability of default by 3%.
Finally, we check for robustness by running a probit model of current default
on past default and past explanatory variables. The results in Table (2.7.1.6) reports
our findings. Column 1 of Table (2.7.1.6) shows our result where we include past
default, past external debt-GDP ratio and past real GDP growth as control variables.
The result shows that the coefficient on past default is positive and significant at 1%
whilst the coefficient on corruption is positive but insignificant. The coefficient on
political stability is positive and significant at 5%. Using the corresponding marginal
effect column in 4 of Table (2.7.1.6), the estimated probability effects of corruption and
political stability are 0.031 and 0.026, insignificant and significant at 5%, respectively.
This implies that a unit change in corruption will increase the probability of default
by 3%, similarly a unit change in political stability will increase the probability of
default by 3%. When we include past default, past external debt-GDP ratio and past
GDP per Capita as control variables, as displayed in column 2 of Table (2.7.1.6), the
38
coefficients on past default and political stability are positive and significant at 1%
and 5% respectively whilst the coefficient on corruption is positive but insignificant.
Using the corresponding marginal effect column in 5 of Table (2.7.1.6), the estimated
probability effects of corruption and political stability are 0.034 and 0.025, insignificant
and significant at 5%, respectively. This implies that a unit change in corruption will
increase the probability of default by 3%, similarly a unit change in political stability
will increase the probability of default by 3%. The result in column 3 of Table (2.7.1.6)
displays our findings where we include past default, past external debt-GDP ratio, past
real GDP growth and past GDP per Capita as control variables. We find that whilst
the coefficients on past default and political stability are positive and significant at
1% and 5% respectively, the coefficient on past corruption is positive and significant
at 10%. Using the corresponding marginal effect column in 6 of Table (2.7.1.6), the
estimated probability effects of corruption and political stability are 0.038 and 0.025,
significant at 10% and 5%, respectively. This implies that a unit change in corruption
will increase the probability of default by 4%, similarly a unit change in political
stability will increase the probability of default by 3%.
The coefficients on corruption and political stability are positive in all cases, an
indication that higher corruption and political stability are associated with a higher
sovereign default probability. The general conclusion to be drawn is that this not
only implies that there is a positive association with sovereign default and, corruption
and political stability, but that there is persistence in this relationship. In particular,
past default, corruption, political stability and macroeconomic variables tend to have
a significant positive influence on current default–a result which is in line with other
findings (see McFadden et al. (1985); Balkan (1992); Li (1992); Aylward and Thorne
(1998); Lausev et al. (2011) and Pestova (2015)).
2.2.4 Discussion
Taken together, our results suggest that there is a significant positive association
between sovereign default and political risk, controlling for other important determ-
39
inants of default. This central finding remain fairly robust to a battery of sensitivity
analyses, including additional controls and various specifications. However, it should
be emphasised that our results do not imply causality. The reason for this is that there
could be endogeneity (e.g. measurement issues, simultaneity etc.) in the specifications
we adopted above. Unfortunately, the nature of our sample (e.g. emerging markets)
and dataset mean that this issue cannot be effectively resolved. The main challenge
we face relates to the issue of finding suitable instruments for political risk indicat-
ors, including corruption (i.e. institutional quality). Fortunately enough, our model
specifications are consistent with many studies (see Balkan (1992); Li (1992); Verma
(2002) and Lausev et al. (2011)), on this area, which have not used instruments for
institutional variables.
This paper provides empirical evidence about the importance of corruption and
political factors on predicting sovereign default probabilities of emerging economies.
Emerging economies have become an important investment destination in recent times.
Estimating models that can provide sign of sovereign default probabilities would be of
interest to investors. Overall, our results show that emerging economies that want to
reduce their probabilities of default, the cost of borrowing and improve access to credit,
should generally:
1) Control and reduce corruption, attract more Foreign Direct Investments and
stimulate GDP growth.
2) Have a good repayment habit by reducing the size of the external debt-GDP
ratio and avoid sovereign default on debt resulting from unwillingness rather than
inability to repay.
One recommendation for future research concerns the specification of the econo-
metric model itself. We could improve the model by including more specific political
risk factors as explanatory variables, such as number of armed conflicts in the country
during the sample period and/or the number of political turnovers of the government.
Finally, we could include more financial market variables to improve the accuracy of
the models.
40
2.3 The Theoretical Model
We consider an economy with infinitely-lived households and alternating types of gov-
ernment. The basic structure of our model follows that of Eaton and Gersovitz (1981),
as used recently by Arellano (2008), Yue (2006), Aguiar and Gopinath (2006) and
Hatchondo et al. (2009). Our model differs from those frameworks by incorporating
government expenditures and government corruption into the analysis of sovereign de-
fault. The theoretical model intends to replicate the main empirical observations.
The basic assumption is that the central government borrows from the inter-
national financial market to smooth consumption of households through trading of
non-contingent bonds. There is a single tradable good and a stochastic endowment
stream of income. The government has an opportunity to default on its debt and
thereby avoid making debt repayments. However, doing this is costly as it leads to a
loss in output in the following period.
Corruption takes the form of a government’s pilfering of public funds raised
through high taxes. There exist two types of political rulers which alternate in power
and which differ according to their propensity to be corrupt. Both types are partially
benevolent in the sense that they care about the utility of households and also extract
corrupt consumption. At the beginning of period a corrupt ruler in power observes
the current state of the economy and borrows to smooth consumption of households.
During this period, ruler observes the realisations of shocks and the level of debt, and
decides whether or not to default. If default is chosen, the economy subsequently suffers
an output loss and lower bond prices. At the end of the period, there is an exogenous
probability that the ruler will be replaced by the alternative government.
2.3.1 The Government’s Decision Problem
There is a single tradable good in the economy. The economy receives a stochastic en-
dowment y, which follows an AR(1) around a long run mean µy, and evolves according
to
41
log(yt) = (1− ρ)µy + ρy log(yt−1) + εt
|ρy| < 1, and εt ∼ N(0, σ2ε).
The government finances its budget through taxes on output. In addition to tax income,
the government has access to financial assets in the form of one-period non-contingent
bonds.
We differ from Cole et al. (1995), Alfaro and Kanczuk (2005), and Hatchondo et al.
(2009) in assuming that two types of policymakers with different levels of corruption
alternate in power. When in power, the objective of the policymaker is to maximise
the present discounted value of future utility flows, on behalf of the households. There
is a probability πj that at the end of every period the type of policymaker in power will
change. Unlike Hatchondo et al. (2009), in our model the value of πj is state dependent,
where j ∈ {L,H} denotes the government type. More corrupt policymakers are able
to loot cgH from the state coffers whilst at the same time face a probability of πH of
being replaced. The less corrupt policymakers are able to loot cgL from the state coffers
whilst at the same time face a lesser probability of πL of being replaced, where cgH > cgL
and πH > πL.
Thus far, this set-up helps compare our model to recent models of political in-
stability and sovereign default, but also illustrates the crucial role played by corruption
as a determinant of sovereign default. The policymaker in power determines how much
to borrow for the following period and whether to pay back previously issued debt. Fin-
ancial assets available to the policymaker are in the form of one-period non-contingent
bonds. A bond issued in the current period delivers one unit of the good in the next
period if no default. At the beginning of the period, the economy has bond position
denoted by b. In the previous period if the country was an issuer of bonds, the value
of b is negative.
Following others (see Aguiar and Gopinath (2006); Hatchondo et al. (2009)), we
consider defaulting to be costly because it imposes a direct output loss on the economy
in the future. This assumption that countries suffer an output loss following a default is
meant to capture any disruptions in economic activity resulting from a default decision.
42
We denote this output loss by λ percent2.
Information on the type of government and the economy’s endowment is perfectly
available to lenders. There is a continuum of risk-neutral lenders in the international
financial market and lenders can borrow or lend at the risk-free rate r. The bond price
is determined when the government determines how many bonds to issue and sells to
the lender that offers the highest price. We denote as qjd(y, b′) the price offered when
ruler j issues a total of −b′ of bonds. This price depends on whether the country
currently has defaulted (d), current endowment realisation y and asset choice b′ but
does not depend on default decisions in previous periods because we assume that the
effect of a default on output only lasts for one period and lenders are forward looking.
We specify how this price is determined later in Section (2.3.3).
The government’s budget constraint in a given period is summarised by:
c+ cgj + qjd(y, b′)b′ ≤ (1− hλ)y + (1− d)b (2.3.1.1)
where c is household consumption and cgj is ruler j′s corrupt consumption. y is output,
b is existing assets (negative if borrowing) and d is default. d = 1 if the government
is defaulting on its existing debt, otherwise it is 0. h is the history of default, where
h = 1 if the government defaulted in the previous period, and 0 otherwise. qjd(y, b′) is
the bond price for ruler j in power. This price depends on whether the country cur-
rently has defaulted (d), current endowment realisation y and asset choice b′. Corrupt
consumption cgj is expressed as:
cgj = τj(1− hλ)y
2
Some of the earliest papers (see Aguiar and Gopinath (2006)) on sovereign default assumed thatλ is the output lost in autarky given that a country is excluded from the financial market afterdefault for stochastic number of periods. Rose (2005) finds evidence that following the initiation ofdebt renegotiation by a country, bilateral trade flows declines by 8% a year. However, some recentpapers such as Hatchondo et al. (2007), Hatchondo et al. (007a), and Hatchondo et al. (2009) thatassume non-exclusion from the financial market, argue that output loss occurs period after default.They argue generally that the assumption of output-loss after default decision is meant to captureany disruptions in economic activity that will be caused by a default. They posit further that asovereign default decreases private sector financing and will thus reduce aggregate output. Alsoas argued in Hatchondo et al. (2007) whether we specify the output loss to be stochastic or onlyone period after default would not make difference. However, we assume in our model it followsthe period after default for simplicity reasons.
43
where τj is the tax rate of ruler j. This assumption of the tax rate being affected
by corruption is grounded in public capital and corruption, and tax avoidance and
corruption literature (see Chen (2003); Coppier et al. (2006); Ellis and Fender (2006);
Attila (2008)). The specification is to capture the effect of corruption consumption,
borrowing and welfare, through taxation and corrupt consumption.
The ruler in power uses the available resources, after corrupt consumption, to
maximise life time utility subject to Equation (2.3.1.1), by choosing c and b′. Flow
utility of government j is CRRA utility u(c) = c1−ϕ−11−ϕ , where ϕ is the risk aversion
parameter.
At the beginning of the period ruler j in power observes the economy’s endowment
realisation and accordingly makes a default decision on previously issued debt. The
ruler issues an amount −b′j0(b, y, h) of bonds if the decision is not to default. Otherwise,
the ruler issues an amount −b′j1(y, h) of bonds. The type of ruler in power changes
with a probability of turnover rate πj or otherwise sticks to power at the rate (1− πj),
before the next period. In our setting, the probability of turnover is allowed to depend
on the type of government in power. In light of this, the more corrupt ruler faces an
economy with higher political instability than the less corrupt ruler. As stated earlier,
in the follow-up period after a default, the economy suffers an output loss of λ percent.
Ruler j in power compares the value functions Vj1(y, h), if a default is declared
in the current period and Vj0(b, y, h), if a default is not declared in the current period;
where y is the current endowment realisation, and h the credit history.
2.3.2 Solution
We use the value function iteration method to solve the dynamic problem. Let Vj(y, b, h)
denote the value function of a government of type j at the beginning of period t when
in power. Similarly, let Vj(y, b, h) denote the value function of a government of type j
at the beginning of period t when it is not in power. Finally, let πj denote the probab-
ility of political turnover of a government of type j. When deciding whether to default,
the government in power compares two continuation values, Vj1(y, h) and Vj0(y, b, h).
44
Vj1(y, h) is the value the government would receive if the type j government defaults in
the current period. Vj0(y, b, h) is the value the government would receive if it did not
default in the current period. Since the two government types may differ, the value
functions Vj and Vj do not need to coincide.
The value of a type-j government of defaulting in the current period is given by:
Vj1(y, h) = maxc, b′{u(c) + βE[πjVj(y
′, b′, 1) + (1− πj)Vj(y′, b′, 1)|y]}
(2.3.2.1)
subject to
c+ cgj + qj1(y, b′)b′ = (1− hλ)y
where cgj = τj(1− hλ)y
Since the government is defaulting, d = 1 in Equation (2.3.1.1). The government then
chooses c and b′ subject to this budget constraint. The associated policy functions are
cj1(y, h) and b′j1(y, h).
The value of a type-j government of not defaulting in the current period is given by:
Vj0(y, b, h) = maxc, b′{u(c) + βE[πjVj(y
′, b′, 0) + (1− πj)Vj(y′, b′, 0)|y]}
(2.3.2.2)
subject to
c+ cgj + qj0(y, b′)b′ = (1− hλ)y + b
where cgj = τj(1− hλ)y
Since the government is not defaulting, d = 0 in Equation (2.3.1.1). The government
then chooses c and b′ subject to this budget constraint. The associated policy functions
are cj0(y, b, h) and b′j0(y, b, h).
The value function of the government in power, Vj(y, b, h) is then computed as follows:
Vj(y, b, h) = max(Vj1(y, h), Vj0(y, b, h)) (2.3.2.3)
where d = 1 if Vj1(y, h) ≥ Vj0(y, b, h) (government defaults). Otherwise d = 0. Let
dj(y, b, h) denote the associated policy function:
45
dj(y, b, h) =
1 if Vj1(y, h) ≥ Vj0(y, b, h)
0 if Vj1(y, h) < Vj0(y, b, h)
(2.3.2.4)
Remaining policy functions are:
cj(y, b, h) =
cj1(y, h) if dj(y, b, h) = 1
cj0(y, b, h) if dj(y, b, h) = 0
b′j(y, b, h) =
b′j1(y, h) if dj(y, b, h) = 1
b′j0(y, b, h) if dj(y, b, h) = 0
The value function of government of type j when it is not in power depends
on the optimal behaviour of the other government, denoted by −j. The value of a
policymaker of type j when it is not in power can be more concisely written as:
Vj(y, b, h) = u(c−j(y, b, h))+
βE[π−jVj(y′, b′−j(y, b, h), d−j(y, b, h))+
(1− π−j)Vj(y′, b′−j(y, b, h), d−j(y, b, h))|y]
(2.3.2.5)
When policymaker j is not in power, it receives no corrupt consumption, but it still
derives utility from household consumption (which is chosen by the other policymaker).
Next period, with probability π−j, policymaker j will become the government in power,
in which case it’s initial state will depend on the actions of the current government.
With probability 1 − π−j, policymaker j will still be out of power. In that case, its
state is still determined by the actions of the government in power.
2.3.3 Bond Price
We define pdefj (y, b′, h′) to be the probability that the type-j government (if it is in
power next period) will default on the debt b′ tomorrow with history h′ given current
endowment realisation y.
46
pdefj (y, b′, h′) =
∫dj(y
′, b′, h′)f(y′|y)dy′
where f(y′|y) is the probability density function for y′.
The bond price qjd(y, b′) satisfies the lender’s zero-profit condition.
qjd(y, b′) =
1
1 + r[1− πjpdef−j (y, b′, d)− (1− πj)pdefj (y, b′, d)] (2.3.3.1)
Bond prices today depend on the credit history the future government will inherit (h′)
because defaulting in the current period reduces future output. The credit history h′
just reflects the current default decision (i.e. h′ = d). This price qjd(y, b′) reflects two
things. First, with probability πj, the other government will be in power and it will
default with probability pdef−j (y, b′, d). However, with probability (1 − πj), the current
government will remain in power, and it will default with probability pdefj (y, b′, d).
2.3.4 Equilibrium
Governments act sequentially when choosing current levels of taxes, corrupt consump-
tion and debt with foresight. Drawing on the works of Krusell and Smith Jr (2003),
Klein et al. (2008), and Ortigueira et al. (2012) we will concentrate on differentiable
Markov-perfect equilibria of this economy. However, as it is shown in Krusell and
Smith Jr (2003) there is a problem of indeterminacy of Markov-perfect equilibria in
an economy with infinite horizon. Hatchondo et al. (2009) argue that the problem is
avoided analysing the equilibrium that arises as the limit of the finite-horizon economy
equilibrium.
A Markov-perfect equilibrium is defined as:
(1) the set of value functions Vj(y, b, h), Vj0(y, b, h), Vj1(y, h) and Vj(y, b, h) for all
j = L,H
(2) the policy functions cj0, cj1, b′j0(y, b, h), b′j1(y, h) and the default decision rule
dj(y, b, h) for all j = L,H
47
(3) and the bond price qjd(y, b′) for all j = L,H,
such that
(a) the value functions Vj(y, b, h), Vj0(y, b, h), Vj1(y, h) and Vj(y, b, h) satisfy the func-
tional Equations in (2.3.2.1), (2.3.2.2), (2.3.2.3), (2.3.2.4), (2.3.2.5) and (2.3.3.1).
(b) the policy functions cj0, cj1, b′j0(y, b, h), b′j1(y, h) and dj(y, b, h) solve the dynamic
programming problem specified in Equations (2.3.2.1), (2.3.2.2), (2.3.2.3), (2.3.2.4),
(2.3.2.5) and (2.3.3.1).
(c) the bond price qjd(y, b′) satisfies the lenders’ zero profit condition in Equation3
(2.3.3.1).
2.4 Results
We show that all defaults may be strategic. In addition, we find that in the presence
of corruption and political turnover, the model performs better in many ways. First,
the model is able to generate the moderate correlation between output and default
decisions as it is documented by Tomz and Wright (2007), the latter also influenced
by the level of corruption. Second, the model helps in generating lower issuance levels
after a default episode. Third, the model is able to generate higher but volatile spreads.
Overall, both corruption and political turnover are important in order for the model
to generate higher credit spreads, higher default rates and more volatile interest rates.
2.4.1 Calibration
We solve the model using value function iteration in Fortran 90 (see Appendix (2.6)
for details and Appendix (A.1) for the codes). We calibrate the model to match a typ-
ical emerging economy that is known for corruption and also has history of sovereign
default. Our calibration is summarised in Table (2.4.1.1) and most calibrated para-
meters are based on Hatchondo et al. (2009). The output loss parameter associated
with default is taken to be 8.3%. The risk-free interest rate is set at 1% whilst we
3As in the literature (see Hatchondo et al. (2007); Hatchondo et al. (2009)), we assume the risk-freeinterest rate is such that β(1 + r) < 1.
48
choose a discount factor of 0.90 equal to the discount factor used by Hatchondo et al.
(2009) for a patient type, and greater than the discount factor (0.80) used by Aguiar
and Gopinath (2006).
We calibrate the tax rates of the less corrupt and more corrupt rulers to be 22%
and 50%, respectively. In our case, the degree of political stability is state dependent
(unlike Hatchondo et al. (2009)), and as such, varies with the level of corruption. The
more corrupt government stays in power for an average duration of 4 years and 3 years,
respectively, under stable and unstable economies. On the other hand, the less corrupt
government stays in power for an average duration of 8 years and 6 years, respectively,
under stable and unstable economies.
2.4.2 Corruption, Political Risk and Default Risk
Our first line of inquiry concerns the question of whether changes in the political
environment associated with changes in the level of corruption can trigger sovereign
default. Cole et al. (1995); Alfaro and Kanczuk (2005); Hatchondo et al. (2009) show
that political circumstances can trigger sovereign default. Hatchondo et al. (2009)
argue that sovereign default is likely to be caused by political turnover4 if there enough
political stability in the economy. We add to their findings by showing that corruption
could be a trigger for sovereign default not only when there is political turnover but
without political turnover. We simulate the model for 1,500,000 periods (1,000 samples
of 1,500 observations each) using the calibrations in Table (2.4.1.1) in order to show
our results.
We show that when there is political stability but a possibility of political turnover,
a change in regime from a less corrupt government to a more corrupt government is
more likely to trigger default than a change in regime from a more corrupt government
to a less corrupt government. In the economy with high political stability, changes from
4
Government turnover rate is the probability with which a government is replaced. Political/Gov-ernment stability on the other hand, is how big or small a turnover rate is. For instance a smallerturnover rate will mean more stability. In the extreme case 0 will mean no turnover but moststability.
49
Table
2.4.1.1.:
Cal
ibra
tion
Des
crip
tion
Par
amet
erV
alue
Ris
kA
vers
ion
ϕ2
Inte
rest
Rat
er
1%A
uto
corr
elat
ion
Coeffi
cien
tρy
0.95
Sta
ndar
dD
evof
Innov
atio
ns
σε
2.7%
Outp
ut
Los
sλ
8.3%
Dis
count
Fac
tor
β0.
90M
ean
(Log
)O
utp
ut
µy
−1 2σ
2 ε
Tax
Rat
eof
Les
sC
orru
pt
Gov
ernm
ent
τ L22
%T
axR
ate
ofM
ore
Cor
rupt
Gov
ernm
ent
τ H50
%Sta
ble
Eco
nom
y’s
Turn
over
Rat
efo
rL
ess
Cor
rupt
Gov
ernm
ent
πs L
3.1%
Unst
able
Eco
nom
y’s
Turn
over
Rat
efo
rL
ess
Cor
rupt
Gov
ernm
ent
πu L
4.4%
Sta
ble
Eco
nom
y’s
Turn
over
Rat
efo
rM
ore
Cor
rupt
Gov
ernm
ent
πs H
7.0%
Unst
able
Eco
nom
y’s
Turn
over
Rat
efo
rM
ore
Cor
rupt
Gov
ernm
ent
πu H
10%
50
a less corrupt to a more corrupt government triggers default 95.5% of the time, whereas
in an unstable economy, default happens only 2% of the time (see Table (2.7.1.7)). In
the stable economy, it is more likely that the less corrupt policy maker will choose high
debt levels which would lead to a more corrupt policy maker to default.
We have to make certain specific assumptions about certain variables in order to
be able to present some of our results in two-dimensional charts. However, the results
will not change much under alternative assumptions.
There are combinations of debt levels and endowment realisations at which a
more corrupt type defaults and a less corrupt type does not default. For a combina-
tions of debt levels and endowment realisations where the less corrupt type chooses to
default, the more corrupt type will also choose to default. Figure (2.4.2.1) depicts the
value of default and the value of not defaulting for the less corrupt and more corrupt
governments. The value of default does not depend on debt, and is therefore depicted
by horizontal lines, because initial debt becomes zero after a government defaults. The
upward sloping curves depict the expected utility of both governments. They show
that the expected utility decreases with debt when governments do not default. The
line depicting the value of not defaulting for the less corrupt government lies above
the line depicting the value of not defaulting for the more corrupt government. This
implies that there are debt levels (between 0.06 and 0.098) at which the more corrupt
government defaults and less corrupt government does not.
51
−0.12 −0.1 −0.08 −0.06 −0.04 −0.02 00.12
0.14
0.16
0.18
0.2
0.22
Valu
e f
un
cti
on
fo
r
τL
b
−0.12 −0.1 −0.08 −0.06 −0.04 −0.02 00.14
0.16
0.18
0.2
0.22
0.24
Valu
e f
un
cti
on
fo
r
τH
No de faul t, τL
No de faul t, τH
Defaul t, τL
Defaul t, τH
Figure 2.4.2.1.: Value functions in a stable economy under less and more corruptgovernments. The figure assumes the case where the endowment realisation coincideswith unconditional mean of its distribution, and where the government inherits agood credit history (h = 0).
The optimal default decision of the two types of government is also illustrated in
Figure (2.4.2.2). Figure (2.4.2.2) plots default space against debt and endowment real-
isation for more corrupt and less corrupt governments. The dark area shows combina-
tions of bond positions and endowment realisations at which a more corrupt government
defaults and a less corrupt government does not default. The grey area shows com-
binations of bond positions and endowment realisations at which both types default.
The white area shows combinations of bond positions and endowment realisations at
which neither the less corrupt nor the more corrupt government will default. It shows
that default is more likely with more debt and lower endowment realisations. That
is for any given level of corruption and endowment realisation, the risk of default is
52
greater with more debt. Similarly, for any given level of debt and corruption, any type
of government is more likely to default when endowment realisation is low than when
endowment realisation is high. The figure shows that the risk of default is greater with
more corruption; at the same level of debt and endowment realisation, default risk is
higher with more corruption.
Figure 2.4.2.2.: Default space against bond issuance and endowment for less andmore corrupt governments, where they inherit a good credit history (h = 0).
This implies that a more corrupt government is more likely to default on lower level
of debt than a less corrupt government will do. Given enough political stability, the
less corrupt policymaker borrows more and the more corrupt policymaker defaults
upon assumption of office. Another reason is that low corruption reduces government
consumption and this in turn increases private consumption. On the other hand, high
corruption leaves less resources for private consumption and the government has a
53
greater incentive to default and keep the money for itself.
The shape of the bond price function that a government in power faces is affected
by the optimal default strategies of types. Figure (2.4.2.3) presents a plot of the
bond price for less corrupt government under stable and unstable economies, and the
economy without political turnover. The bond price received by the government for
bonds issued is affected by the probability of default the following period, the level
of corruption and the political turnover of the government. As a result, the bond
price functions in economies with political turnover shows three steps. Drawing from
Hatchondo et al. (2009), the right step shows “low” issuance region, where debt issued
is so low that any type of government will surely pay back the following period. Due
to the less risky nature of debt in this region, investor charge the risk-free rate which
results in high bond prices. The middle step shows the “intermediate” issuance region.
In this region, the more corrupt type would default in the following period if he comes
into power, whilst the less corrupt type will choose to pay the debt back if he remains
in power. In this region lenders charge positive spread which depends on the turnover
rate (which is dependent on the government type). This is to say that the more corrupt
government is charged higher spreads than the less corrupt government, for instance,
in a politically stable economy. For a given level of corruption, the spread is higher
in the unstable economy than the stable economy. However, the higher the level of
corruption the higher the spread for each type of economy.
The third step is the “high” issuance region, where both types will default next
period when in power. Consequently, lenders offer low price for bonds issued in this re-
gion. Figure (2.4.2.3) shows that in the “intermediate” region of issuance the better the
price, the more politically stable the economy is. With chances that the more corrupt
assumes power the following period and declares default, the less corrupt government
issuing bonds in this region would have to compensate lenders for default contingency.
An increase in the probability of this contingency results in a decrease in bond price
in the “intermediate” region and the vice versa. The bond price does not feature the
“intermediate” step where there is no turnover and only the less corrupt government
54
remains in power.
−0.09 −0.08 −0.07 −0.06 −0.05 −0.04 −0.030.94
0.95
0.96
0.97
0.98
0.99
1
b’
Bond p
rice
No turnove r
πs
L= 3.1%
πu
L= 4.4%
1−πu
L
1+ r
1−πs
L
1+ r
1
1+ r
Figure 2.4.2.3.: Bond price for less corrupt government (τL) in stable and unstableeconomies and in economies without political turnover. The figure assumes thecase where the government has not defaulted today and the endowment realisationcorresponds with the unconditional mean of its distribution.
Figure (2.4.2.4) is a plot of objective function of the less corrupt government as
a function of bond issuance. The shape of this objective function of the government
is related to the shape of the bond price function discussed above. Just as in the
bond price function, the objective function increases at “low” issuance levels, whilst in
transition to the second step from the first step of the bond price function, it decreases.
This accounts for the right local maxima. The objective function begins to increase
again once the second step of the bond price function is reached. As the “high” bond
issuance region of the bond price function is reached, the objective function begins
to decline and remain low, which explains the left local maxima. As explained in
55
Hatchondo et al. (2009) the increasing portions of the objective function are as a result
of the differences between the rate at which future utility flows are discounted and
the interest rate, whilst the decreasing portions are explained by the decline in bond
price as a result of increasing issuance levels. In the politically stable economy, the
optimal borrowing level may occur at the left local maximum, whilst in the politically
unstable economy the optimal borrowing levels may occur at the right local maximum.
The optimal borrowing levels of the less corrupt policymaker in the politically stable
economy is higher and attractive than in the politically unstable economy because as
instability decreases, the less policymaker is charged a lower spread by lenders. This
low spread in a politically stable economy might induce less corrupt policymakers to
choose borrowing levels in the intermediate region which then makes default more likely
when there is change in power to the more corrupt policymaker.
The results in Table (2.4.6.2) displays the expected probabilities of default. It
is observed that, in the stable economy, the probability of default given that the less
corrupt government in power today5 is about 11.13%, whereas the probability of de-
fault given that the more corrupt government in power today is about 0.44%. However,
in the politically unstable economy, the probability of default given that the less cor-
rupt government in power today is about 0.32%, while the probability of default given
that the more corrupt government in power today is about 0.48%. Similarly, in the
politically stable economy, the average number of defaults given that the less corrupt
government is in power today is about 0.20%, while the average number of defaults
given that the more corrupt government in power today is about 0.84%. In the polit-
ically unstable economy, however, the average number of defaults given that the less
corrupt government is in power today is about 0%, while the average number of defaults
given that the more corrupt government in power today is about 0.48%. Overall, the
higher credit spreads faced by the low type in the stable economy reflect the probability
that the high type will come into power next period and default.
5This probability takes into account the possibility that the more corrupt government might bein power tomorrow, but also that the less corrupt government will most likely still be in powertomorrow.
56
−0.1 −0.09 −0.08 −0.07 −0.06 −0.05 −0.04 −0.03 −0.02 −0.01 04.49
4.5
4.51
4.52
4.53
4.54
4.55
b’
Obje
cti
ve f
uncti
on w
hen π
s L=
3.1
%
−0.1 −0.09 −0.08 −0.07 −0.06 −0.05 −0.04 −0.03 −0.02 −0.01 04.49
4.5
4.51
4.52
4.53
4.54
4.55
Obje
cti
ve f
uncti
on w
hen π
u L=
4.4
%
πs
L= 3.1%
πu
L= 4.4%
Figure 2.4.2.4.: Objective function of a less corrupt government (τL) in the stable andunstable economies. The figure assumes the case where the government has chosennot to default and the endowment realisation corresponds with the unconditionalmean of its distribution, and where the government inherits a good credit history(h = 0).
Figure (2.4.2.5) shows that a less corrupt policymaker chooses intermediate bor-
rowing levels if it encounters intermediate endowment realisations. The right end of the
graph is where the endowment realisation is at its highest and where the less corrupt
policymaker chooses low borrowing level. In other words, when a less corrupt poli-
cymaker faces good economic conditions, political turnover might not trigger default.
The left end of the graph is where the endowment realisation is at its lowest and where
both types of policymakers are likely to default when in power. As the policymaker
defaults and resets its debt level to zero in this low endowment region, it then borrows
less because it has low borrowing needs.
57
−0.05 0 0.05 0.1 0.15 0.20
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Current Productivity
Borr
ow
ing
b = −0.060
Figure 2.4.2.5.: Optimal bond issuance of a less corrupt government (τL) in a stableeconomy. The government inherits a good credit history (h = 0) and a debt level of−0.0385. Issuance decision is determined after an optimal default decision is madeby the type.
2.4.3 Corruption, Welfare and Consumption
Corruption in our model has important implications for welfare and consumption of
the households. We show that corruption has the propensity to negatively affect the
welfare and consumption of the households. Following the seminal work of Lucas
(1987), we estimate welfare loss (consumption equivalent) as the percentage decrease in
consumption in the non-corrupt economy which makes households indifferent between
the corrupt economy and the non-corrupt economy. Table (2.4.3.1) shows the average
household consumption equivalent welfare loss (in percentage terms) for the less and
more corrupt (see Appendix (3.5.5) for detailed derivation of welfare loss). Again,
the results indicate that welfare loss increases with the level of corruption. In other
58
words, the results show how much households are willing to pay (and this amount is
more when a more corrupt policymaker is in office) in order to have corruption-free
consumption. On the whole, the results show that households are willing to give up
(43%) of consumption in the non-corrupt economy when a more corrupt policymaker
is in office and (28%) of consumption in the non-corrupt economy when a less corrupt
policymaker is in office, in order to have corruption-free consumption.
Table 2.4.3.1.: Average Consumption Equivalent Welfare Loss
Level of Corruption Consumption Equivalent Welfare LossτL 28%τH 43%
2.4.4 Characteristics of Debt and Spread around Defaults
We define two types of defaults. The first is a “non-political default”, which is any
default that is not triggered by a change in government. The second, “political default”,
are all the defaults which are triggered by a change in government (see Hatchondo et al.
(2009)). It is argued that during political default, post-default issuance levels are lower
than pre-default issuance levels, whilst in a non-political default there are no differences
between pre-default and post-default issuance levels (see Hatchondo et al. (2009)).
We show results that are consistent with the literature. Figure (2.4.4.1) shows the
differences between pre-default issuance levels and post-default issuance levels under
political and non-political defaults.
Hatchondo et al. (2009) find that if the same government remains in power after
a non-political default, there should not be difference between pre-default and post-
default issuance levels. We find a similar result. We argue that once the type of
borrower (less corrupt government or more corrupt governments) does not change and
is common knowledge to lenders, there is no need to charge different (higher) spreads
which then results in no change in issuance levels. Around political defaults, however,
we find that post-default issuance levels are lower than pre-default issuance levels. We
argue that as the less corrupt government (whose optimal borrowing is in the interme-
diate region) is replaced by the more corrupt government (whose optimal borrowing
59
should be the low issuance region as discussed earlier), post-default issuance levels will
be lower than pre-default issuance levels. As the next policymaker (more corrupt)
prefers to borrow in the low issuance region, we expect lenders to charge low spreads
in the period immediately following a default.
−4 −3 −2 −1 0 1 2 3 40.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
Period
Chan
ge
in I
ssuan
ce o
f B
onds
Political default
Non−political default
Figure 2.4.4.1.: Average issuance level before and after a default episode in an eco-nomy with high political stability. The default period is 0. Political defaults arewhere less corrupt government is replace by more corrupt government, and non-political defaults are where only a less corrupt government is in power.
Figure (2.4.4.2) shows why more corrupt policymaker might choose lower issuance
volumes. The bond price faced by the more corrupt depicts three steps just as the less
corrupt policymaker. If a more corrupt policymaker is in office today, it is very likely
the next policymaker will also be more corrupt. Following our previous assertion that
the more corrupt policymaker defaults at intermediate debt levels, lenders charge high
spread for intermediate borrowing levels. This accordingly, explains why the bond
60
price in the intermediate region is close to zero. Bond price in the low issuance region
is higher than that in the intermediate region which explains why the more corrupt
policymaker will borrow in the low issuance region.
−0.1 −0.09 −0.08 −0.07 −0.06 −0.05 −0.040
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
b’
Bond p
rice
πs
H= 7%
πu
H= 10%
Figure 2.4.4.2.: Bond price faced by a more corrupt government (τH) in the stableand unstable economies. The figure assumes the case where the government hasdefaulted today and the endowment realisation corresponds with the unconditionalmean of its distribution.
Figure (2.4.4.3) shows plots of pre-default and post-default average spread levels.
In political default, post-default spreads are lower than pre-default spreads. Less cor-
rupt policymakers choose intermediate borrowing levels before political default, and as
a result are charged intermediate spreads. The more corrupt replaces the less corrupt
and after a default is declared the more corrupt borrows in the low issuance region
and lenders respond by charging low spreads in the period immediately following a
default. However, if default is non-political, post-default spreads are not different than
61
pre-default spreads because as the type of government does not change, lenders do not
see the need to charge different spreads for the two periods.
−4 −3 −2 −1 0 1 2 3 40
0.2
0.4
0.6
0.8
1
1.2
1.4
Period
Change i
n s
pre
ad
Political default
Non−political default
Figure 2.4.4.3.: Average spread before and after a default episode in an economywith high political stability. The default period is 0. Political defaults are whereless corrupt government is replace by more corrupt government, and non-politicaldefaults are where only a less corrupt government is in power.
2.4.5 Output and Default
Tomz and Wright (2007) in their studies using data set with 169 default cases, report
that 38% of default episodes in their sample occurred in years when the output level in
the defaulting country was above the trend value. However, the inability to replicate
the weak correlation observed in the data, they argue is as a result of the absence of
turnover in their baseline model. To illustrate this, Hatchondo et al. (2009) report
that only 3% and 7% of default episodes occur where all policymakers are patient and
impatient respectively, in periods where the output level is above its long-run mean and
62
when there is no turnover. Table (2.4.5.1) illustrates our findings. We find that only
6% of defaults episodes occur in periods where the output level is above its long-run
mean when all policymakers are less corrupt. This percentage decreases to 5.3% when
all policymakers are more corrupt.
Introducing political turnover into their model, Hatchondo et al. (2009) find that
in an economy with high political stability, 38% of default episodes occur in periods
where output is above its long-run mean and this decreases to 7% in an unstable
political economy. We find that in a politically stable economy when less corrupt poli-
cymakers are in power, 3.57% of defaults episodes occur in periods where the output
level is above its long-run mean. This increases to 46.85% when more corrupt policy-
makers are in power. In politically unstable economy when less corrupt policymakers
are in power, we find that 0% of defaults episodes occur in periods where the output
level is above its long-run mean. This percentage increases to 7.45% when more corrupt
policymakers are in power. Overall, we find that in a stable political economy, 45.93%
of default episodes occur in periods where output is above its long-run mean and this
decreases to 7.45% in an unstable political economy.
Table 2.4.5.1.: Fraction of Default Episodes above Long-Run Mean
τL only τH only πsL = 3.1% πsH = 7.0% πuL = 4.4% πuH = 10%6.00% 5.30% 3.57% 46.85% 0.00 % 7.45%
All Stable All Unstable
- - 45.93% 7.45%
Default episodes that occur when output is above its long-run mean.
2.4.6 Corruption, Political Turnover and Business Cycle Statistics
We now look at the implications of corruption for business cycles in the economy.
Most studies of sovereign default place emphasis on the ability of quantitative sov-
ereign default model to replicate the macroeconomic characteristics of emerging eco-
nomies before a default. We discuss how the predictions of our baseline model change
when we introduce political turnover. To show this, we simulate economies without
turnover–where the type of policymaker in power does not change (i.e. π = 0)–and
compare these simulations with economies with political turnover (i.e. π > 0 ).
63
To compare quarterly simulated data to that of Nigeria for the period 1993Q1-
2000Q4, we simulate the model for 1,000 samples each with 1,500 observations (quar-
ters). Nigeria is used as a benchmark because of its long history of corruption and
political disturbance. In addition, Nigeria has reportedly defaulted as many as five
times6 (in 1982, 1986, 1992, 2001 and 2004). We compare data from this period with
data from simulation samples where only less corrupt policymakers are in power. Ad-
ditionally, we also show simulation results for an economy with only more corrupt
policymakers. Further, we present simulation results with political turnover and ex-
tract the first 1,000 samples with 32 quarters, when the type of government in power
is either the less corrupt or the more corrupt. Finally, we present unconditional results
using the first 1000 samples with 32 quarters without imposing any restriction on the
type of policymakers in power.
High, volatile, and countercyclical interest rates; highly volatile relative consump-
tion; countercyclical net exports are some of the stylised facts of emerging economies.
Table (2.4.6.1) documents our results. We present trade balance as a fraction of output
(TB/Y ), annual interest rate spread Rs, logarithm of income (y), logarithm of con-
sumption (c), mean probability of default Pr(D), mean number of defaults E(D) and
average spread E(Rs). We HP filter all series with a quarterly smoothing parameter,
1, 600. Standard deviations denoted by σ are reported in percentages. We denote cor-
relations by ρ. The second column of Table (2.4.6.1) shows the moments in the data.
In the third column of the table we present the average business cycle moments in an
economy with only less corrupt policymakers, whilst in the fourth column we present
average moments in an economy with only more corrupt policymakers. In the fifth
column are the average business cycle moments under a less corrupt policymaker in a
stable economy with turnover rate of πsL = 3.1%. The sixth column reports the aver-
age business cycle moments under a less corrupt policymaker in an unstable economy
6 As is reported in Standard and Poors, Moodys, World Bank Development Indicators, the IMF and
World Bank–Global Development Finance (1991, 2006, 2012).
64
with turnover rate of πuL = 4.4%. Finally, the seventh and eighth columns display the
unconditional average business cycle moments in a stable economy and an unstable
economy, respectively.
The moments of the data as reported in Table (2.4.6.1) display the striking fea-
tures of a developing economy like Nigeria: counter-cyclicality of net exports (-0.21 )
and interest rate spreads (-0.64); and the pro-cyclicality of consumption (0.15). An-
other striking feature of the business cycles of Nigeria as displayed in the data is the high
volatility of output (1.40%), consumption (5.60%) and interest rate spreads (11.62%),
which are typical stylised facts of developing economies. In particular, these features
about interest rate spreads including their high volatility have been observed by others
including Perri and Neumeyer (2004) to be true for many emerging economies.
In the presence of political turnover and corruption, the ability of the model to
generate high spreads is improved. The average spread observed when less corrupt
policymaker is in office in the politically stable economy is 12.86%, compared with
0.37% in the politically unstable economy. When we compare this to the case when
only less corrupt policymakers are in office, the average spread is 0.33%. As we argued
above, in the politically stable economy, the less corrupt optimally will borrow in the
high issuance region which leads to default when the more corrupt policymaker takes
office. Consequently, lenders charge the less corrupt higher spreads in the politically
stable economy than in the politically unstable economy.
In the stable economy, average spread observed by the less corrupt policymaker
(12.86%) is higher than the average spread observed by the less corrupt policymaker
(0.33%) and the more corrupt policymaker (0.33%), when political turnover is absent.
In the economy where all governments are less corrupt, the average spread is 0.33%.
Similarly, in the economy where all governments are more corrupt, the average spread
is 0.33%. Corruption and political turnover act as the mechanism through which the
model generates a higher average spread. In the model, political turnover amplifies
the effect of corruption because with a low turnover rate, less corrupt governments
are willing to pay the premium for the possibility that a more corrupt government
65
Table
2.4.6.1.:
Busi
nes
sC
ycl
eSta
tist
ics
Eco
nom
y
Sta
tist
icD
ata
No
Turn
over
No
Turn
over
Sta
ble
Unst
able
Sta
ble
Unst
able
τ Lon
lyτ H
only
τ Lτ L
Unco
ndit
ional
Unco
ndit
ional
σ(y
)1.
403.
183.
183.
163.
153.
183.
18σ
(c)
5.60
3.27
3.27
3.23
3.20
8.25
9.65
σ(TB/Y
)0.
600.
150.
10.
160.
110.
330.
11σ
(Rs)
11.6
20.
180.
170.
470.
322.
020.
26ρ(c,y
)0.
151.
001.
001.
001.
000.
340.
31ρ(TB/Y,y
)-0
.21
-0.3
6-0
.36
-0.2
8-0
.27
-0.1
1-0
.26
ρ(Rs,y)
-0.6
4-0
.1-0
.09
-0.1
5-0
.14
-0.0
6-0
.07
ρ(Rs,TB/Y
)0.
10-0
.04
-0.1
0-0
.12
-0.1
7-0
.05
-0.0
9E(Rs)
9.60
0.33
0.33
12.8
60.
376.
690.
37E(D
)-
0.24
0.23
0.20
0.00
5.91
0.28
Pr(D
)-
0.32
0.33
11.1
30.
325.
820.
37
Mom
ents
from
the
mod
elar
eav
erag
esu
sin
g1,0
00
sam
ple
sof
32
per
iod
sea
ch.
Inco
lum
ntw
ow
eu
sed
ata
for
Nig
eria
from
1993Q
1-2
000Q
4.
Exce
pt
corr
elat
ion
coeffi
cien
ts,
all
stat
isti
csare
inp
erce
nta
ges
.
E(D
)is
mea
nnu
mb
erof
def
ault
sp
eran
nu
m.
Pr(D
)is
mea
np
rob
abil
ity
ofd
efau
ltp
eran
nu
m.
Ave
rage
spre
ad,E(Rs)
and
vola
tili
tyof
spre
ad
,σ
(Rs)
are
per
an
nu
m.
Res
tof
stat
isti
csar
equar
terl
y.
66
will default. Also, political turnover impacts on the ability of the model to generate
a higher average spread because it smoothes out the bond price function Hatchondo
et al. (2009).
The smoother bond price function results in a larger increase in the issuance level
when there is a decrease in the bond price. Given that corrupt policymakers have the
incentive to issue more debt, lower bond prices make it attractive for them to do so
and pay a higher spread. Tables (2.4.6.1) and (2.4.6.2), display the non-monotonic
relationship between the degree of political stability and both the average spread and
default probability. Starting with column 3 in Table (2.4.6.1), where a less corrupt
policymaker is in power in the first period and where turnover is absent; i.e. π = 0, an
increase in the turnover rate to πsL = 3.1% increases the average spread from 0.33% to
12.86%. The average spread decreases to 0.37% when turnover rate increases to πuL =
4.4%. Similarly, starting with the case of no turnover in Table (2.4.6.2), an increase in
the turnover rate to πsL = 3.1% increases the average probability of default from 0.32%
to 11.13% which decreases to 0.32% when turnover rate increases to πuL = 4.4%. Does
it mean that default is likely to occur in an unstable economy and under more corrupt
policymakers? Using the average spreads discussed above as a proxy for default, the
answer will likely be no. The average spreads and probabilities of default in Tables
(2.4.6.1) and (2.4.6.2) appear to be higher in the politically stable economy than in
the politically unstable economy. In the stable economy, less corrupt governments pay
high spreads than in the unstable case, despite the fact they are less likely to default.
However, as can be seen from Table (2.4.6.2), less corrupt governments pay higher
spreads to compensate lenders for the possibility that a more corrupt government will
come into power next period and default. Similarly, in the stable economy, the average
probability of default is higher when a less corrupt government is in power. However,
in a stable economy, the average default episodes are higher when a more corrupt
policymaker is in power than when a less corrupt policymaker is in power, but smaller
than the unconditional case (see Table (2.4.6.2)).
As we argued above, corruption affects the outcome of our model in many ways
67
Table 2.4.6.2.: Default Risk Statistics
Economy
StatisticNo Turnover No Turnover Stable Unstable
τL only τH only - -E(Rs) 0.33% 0.33% 6.69% 0.37%E(Rs|τL is in Power) 0.33% - 12.86% 0.37%E(Rs|τH is in Power) - 0.33% 0.43% 0.46%E(D) 0.24% 0.23% 5.91% 0.28%E(D|τL is in Power) 0.24% - 0.20% 0.00%E(D|τH is in Power) - 0.23 % 0.84% 0.48%Pr(D) 0.32% 0.33% 5.82% 0.37%Pr(D|τL is in Power) 0.32% - 11.13% 0.32%Pr(D|τH is in Power) - 0.33% 0.44% 0.48%
E(D) is mean number of defaults per annum.
Pr(D) is mean probability of default per annum.
E(Rs) is expected spread per annum.
including the ability to raise the turnover rate, π, reducing households disposable
income and welfare. Political turnover, on the other hand, as observed by Hatchondo
et al. (2009) works through two forces to impact on the mean spread. Firstly, an
increase in both corruption and turnover results in an increase in the spread paid at
intermediate borrowing levels. Secondly, an increase in turnover and corruption makes
the intermediate borrowing levels less attractive to policymakers. When turnover is low,
policymakers choose intermediate borrowing levels and therefore changes in turnover,
π, are more effective in affecting the spread when turnover, π, is small to begin with.
When turnover, π, is large to begin with, the second effect of turnover and corruption
dominates, as the intermediate region becomes less attractive.
Further more, Table (2.4.6.1) displays the volatility of the model. In the presence
of political turnover, the model is able to generate higher spread volatility. When a
less corrupt policymaker is in office, the standard deviation of the spread is 0.47% in
the economy with high political stability, whereas in the economy with low political
stability the standard deviation of spread is 0.32%. In contract, in the economies
without political turnover, the standard deviation of spread is 0.18% where only less
corrupt governments are in office and 0.17% where only more corrupt governments are
in office. Yet, spread is most volatile, (2.02%), in the politically stable economy without
68
any restriction on the type of government in power. Consumption appears to be most
volatile in the politically stable and unstable economies (columns 7 and 8 of Table
(2.4.6.1)) without restriction on the type of government in power. Similarly, trade
balance is most volatile in the politically stable economy (column 7 of Table (2.4.6.1))
without restriction on the type of government in power. However, the introduction
of corruption and political turnover do not significantly affect some business cycle
moments including output. Both the level of corruption and political turnover play
a major role in generating higher volatility in the model. Additionally, we observe a
very strong (positive) correlation between output and consumption in the cases with
turnover, when a less corrupt government is in power and for the cases without turnover
(when only a less corrupt policymaker or only a more corrupt policymaker is in office).
However, the correlation between output and consumption is weaker when there is
turnover without restriction on the type in power. Also, we find a counter-cyclical
relationship between output and trade balance. Finally, we find a weak and counter-
cyclical relationship between spread and both output and trade balance.
2.5 Conclusion
The principal aim of this paper is to explain how the incidence of corruption might
impact on sovereign borrowing and default decisions. Our empirical analysis provides
strong evidence that higher levels of corruption and political stability are conducive to
higher risks of default, and our theoretical analysis shows that corruption can generate
significant risks of default and credit spreads when there is enough political stability
We establish that a change in power from a less corrupt to a more corrupt government
is more likely to cause default than the reverse. We establish that welfare loss to
households increases in the level of corruption. The policy implication of the paper is
that corruption and government spending have important roles to play in explaining
sovereign default. Efforts by international organisations to prevent sovereign debt crises
should not only involve assistance in the design of better fiscal policies, but also tackle
the root cause of the problem which is corruption.
69
2.6 Appendix A
2.6.1 Computational Method
This section describes the computational method we have used to solve the model. We
solve the government’s problem by value function iteration using grid search technique
over 200 grid points for bond position and 30 grid points for the endowment shock. In
the model simulation, we use 1, 000 samples of 1, 500 periods each. To approximate
output we use the Tauchen (1986) approximation process. The computation is done in
Fortran 90.
We discretise the asset space into 200 grid points [b, b] and endowment space into
30 grid points [y, y] . We choose a relative error tolerance level, ε = 10−6. We start
with an initial guess for the value functions: value of being in power V (0), value of
default V(0)d , value of no default V
(0)nd , and value of being in opposition V 0. We use grid
search over the endowment and asset grids to locate the maximum values and update
the value functions of being in power: V (1), V(1)d and V
(1)nd . Given these updates we
then also update the policy functions and bond price. Then using the updated value
functions, policy functions and bond price, we update the value of not being in power
V 1.
Finally, we compute the distance, d, between V (0) and V (1); and d, between V 0
and V 1. We then evaluate whether the maximum absolute deviation between the new
and previous continuation values is below the relative error tolerance level ε = 10−6. If
it is, a solution has been found. Otherwise, the optimisation procedure is repeated until
the maximum absolute deviation between the new and previous continuation values is
below 10−6.
Using the results from the iteration we simulate the model for 1, 000 samples of
1, 500 observations each. See Appendix (A.1.2) for details of the code.
70
2.6.2 Consumption Equivalent Welfare Loss
Let λ denote the consumption equivalent of welfare loss, the fraction of consumption
one would be willing to give up in each period in the the economy ruled by a non-corrupt
policymaker.
E(V non-corruptt (λ)) = Et
∞∑t=0
βt
[((1 + λ)ct)
1−ϕ − 1
1− ϕ
]λ shows up every period and we assume it is deterministic and this reduces to:
E(V non-corruptt (λ)) = (1 + λ)1−ϕE
(V non-corruptt +
1
(1− ϕ)(1− β)
)− 1
(1− ϕ)(1− β)
Then we want to find the λ that equates this with expected welfare in a corrupt
economy (with less corrupt and more corrupt policymakers). We have:
(1 + λ)1−ϕ(EV non-corrupt
t +1
(1− ϕ)(1− β)
)− 1
(1− ϕ)(1− β)= E(V corrupt
t )
Then
λ =
E(V corruptt ) + 1
(1−ϕ)(1−β)(E(V non-corrupt
t ) + 1(1−ϕ)(1−β)
) 1
1−ϕ
− 1
If we take the economy with no corrupt policymaker to have higher welfare, then
λ < 0. This means households are willing to give up consumption in the high welfare
economy (with no corrupt policymaker) to have the same welfare as an economy with
lower welfare (with a corrupt economy).
2.7 Appendix B
2.7.1 List of Tables
2.7.1.1 Data Sample and Description of Terms Used in Regression
71
Table 2.7.1.1.: Sample of Defaulting and Debt Rescheduling Countries Used for PanelModel
Country Period Examined Rescheduling+Default
Argentina 1984-2008 9Algeria 1984-2008 1Cote D’ivore 1984-2008 8Cameroon 1984-2008 9Costa Rica 1984-2008 5Dominican Republic 1984-2008 11Ecuador 1984-2008 11Ethiopia 1984-2008 6Gabon 1984-2008 8Gambia 1984-2008 4Indonesia 1984-2008 5Kenya 1984-2008 3Kazakhstan 1992-2008 2Moldova 1992-2008 6Nigeria 1984-2008 10Pakistan 1984-2008 3Paraguay 1984-2008 2Peru 1984-2008 8Russia 1992-2008 6Sri Lanka 1984-2008 1South Africa 1984-2008 2Tanzania 1984-2008 6Uruguay 1984-2008 5Venezuela 1984-2008 6Zambia 1984-2008 11Total 1984-2008 148
The final sample is comprised of 25 countries.
587 observations.
72
Table
2.7.1.2.:
Var
iable
sfo
rE
mpir
ical
Wor
k
Var
iable
Des
crip
tion
Sou
rce
Eff
ect
Def
ault
Sov
erei
gnD
efau
lt/R
esch
edule
Wor
ldB
ank
Dev
elop
men
tIn
dic
ator
s
logG
DP
PC
Log
arit
hm
ofG
DP
per
Cap
ita
Wor
ldB
ank
Dev
elop
men
tIn
dic
ator
s(-
+)
corr
ICR
GIC
RG
mea
sure
ofco
rrupti
onP
olit
ical
Ris
kSer
vic
es(+
)
Pol
ista
bilit
yP
olit
ical
Sta
bilit
yF
reed
omH
ouse
Inte
rnat
ional
(+)
Extd
ebtr
atio
Exte
rnal
Deb
tto
GD
Pra
tio
Wor
ldB
ank
Dev
elop
men
tIn
dic
ator
s(+
)
GD
Pgr
owth
Rea
lG
DP
Gro
wth
Wor
ldB
ank
Dev
elop
men
tIn
dic
ator
s(-
)
ICR
Gis
Inte
rnat
ion
alC
ountr
yR
isk
Gu
ide
GD
Pp
erC
apit
ais
con
stan
t20
00U
Sd
olla
rs
73
2.7.1.2 Empirical Model Results
Table 2.7.1.3.: Summary Statistics
Variable Mean Std. Dev. Min. Max. NDefault 0.252 0.435 0 1 587corrICRG 3.428 1.039 0 6 584Polistability 6 1.891 3 9 575logGDPPC 10.737 2.411 6.726 16.03 581GDPgrowth 0.035 0.044 -0.171 0.183 582Extdebtratio 0.708 0.475 0.032 4.149 573
Table 2.7.1.4.: Probit models; dependent variable: Default - (excluding laggeddefault)
VariableProbit Models: Coefficients Marginal Effects
PROB I PROB II PROB III mfx I mfx II mfx IIIcorrICRGt 0.087 0.113 0.114 0.028 0.036 0.036
[0.065] [0.067]* [0.067]* [0.021] [0.021]* [0.021]*Polistabilityt 0.082 0.079 0.079 0.026 0.025 0.025
[0.035]** [0.035]** [0.035]** [0.011]** [0.011]** [0.011]**Extdebtratiot 0.593 0.602 0.599 0.188 0.190 0.189
[0.127]*** [0.126]*** [0.128]*** [0.040]*** [0.040]*** [0.040]***GDPgrowtht -0.099 -0.203 -0.032 -0.064
[1.318] [1.315] [0.419] [0.416]logGDPPCt -0.037 -0.037 -0.012 -0.012
[0.025] [0.025] [0.008] [0.008]Constant -1.896 -1.584 -1.577
[0.404]*** [0.471]*** [0.473]***Observations 557 556 556 557 556 556
Standard errors in brackets
* p<10%, ** p<5%, *** p<1%
74
Table 2.7.1.5.: Probit models; dependent variable: Default - (excluding laggeddefault)
VariableProbit Models: Coefficients Marginal Effects
PROB I PROB II PROB III mfx I mfx II mfx IIIcorrICRGt−1 0.113 0.128 0.138 0.036 0.040 0.043
[0.066]* [0.068]* [0.068]** [0.021]* [0.021]* [0.021]**Polistabilityt−1 0.097 0.094 0.094 0.030 0.029 0.029
[0.035]*** [0.035]*** [0.035]*** [0.011]*** [0.011]*** [0.011]***Extdebtratiot−1 0.583 0.616 0.587 0.183 0.193 0.183
[0.125]*** [0.124]*** [0.125]*** [0.039]*** [0.039]*** [0.039]***GDPgrowtht−1 -1.908 -2.006 -0.599 -0.627
[1.305] [1.302] [0.410] [0.407]logGDPPCt−1 -0.031 -0.032 -0.010 -0.010
[0.025] [0.025] [0.008] [0.008]Constant -2.018 -1.820 -1.746
[0.410]*** [0.479]*** [0.481]***Observations 556 555 555 556 555 555
Standard errors in brackets
* p<10%, ** p<5%, *** p<1%
Table 2.7.1.6.: Probit models; dependent variable: Default - (including laggeddefault)
VariableProbit Models: Coefficients Marginal Effects
PROB I PROB II PROB III mfx I mfx II mfx IIIDefaultt−1 0.666 0.646 0.649 0.225 0.217 0.218
[0.131]*** [0.131]*** [0.131]*** [0.046]*** [0.047]*** [0.047]***corrICRGt−1 0.102 0.112 0.123 0.031 0.034 0.038
[0.067] [0.069] [0.070]* [0.021] [0.021] [0.021]*Polistabilityt−1 0.083 0.081 0.081 0.026 0.025 0.025
[0.036]** [0.036]** [0.036]** [0.011]** [0.011]** [0.011]**Extdebtratiot−1 0.462 0.500 0.468 0.142 0.154 0.144
[0.128]*** [0.126]*** [0.128]*** [0.039]*** [0.039]*** [0.039]***GDPgrowtht−1 -2.027 -2.110 -0.625 -0.648
[1.326] [1.323] [0.409] [0.406]logGDPPCt−1 -0.025 -0.027 -0.008 -0.008
[0.026] [0.026] [0.008] [0.008]Constant -2.002 -1.853 -1.774
[0.417]*** [0.489]*** [0.490]***Observations 556 555 555 556 555 555
Standard errors in brackets
* p<10%, ** p<5%, *** p<1%
75
2.7.1.3 Theoretical Model Results
Table 2.7.1.7.: Mean Number of Defaults Given Change in Type
Economy
Stable UnstableExpected Number of Defaults Given Change to Less Corrupt 0.00% 0.00%Expected Number of Defaults Given Change to More Corrupt 95.5% 2%
Mean number of defaults per annum.
76
Chapter 3
Limited Contract Enforcement and
Firm Financing
3.1 Introduction
The role that financial factors and financial development play in economic activity has
long been documented in the business cycle literature (see Gertler (1988); Carlstrom
and Fuerst (1997, 1998)). However, this role (such as smoothing fluctuations and en-
hancing productive efficiency) hinges crucially on the existence of good institutions
where financial contracts are well enforced. Hence, when the market for loans has an
imperfection such that agents can choose to default on their debt at an exogenous cost
governed by the quality of institutions, economic development becomes undermined.
Levine et al. (2000) find that contract enforcement promotes financial development,
while the latter is conducive to economic growth. In particular, developing economies
do not only have weak legal institutions to enforce contracts but are also character-
ised by high lending rates, unavailability of capital and a generally risky investment
environment.
There is a broad literature on asymmetric information and agency costs associated
with financial markets (see Bernanke et al. (1999); De Fiore et al. (2011); Carlstrom and
Fuerst (1998, 2001); Carlstrom et al. (2010)). Recent models of agency costs normally
assume that borrowers possess private information which lenders can gain access to
77
only after paying some monitoring or verification cost. This paper seeks to contribute
to the literature on agency costs, asymmetric information and financial development
by studying the role of limited contract enforcement1 in a Dynamic Stochastic General
Equilibrium (DSGE) framework. We do so by allowing for the possibility of the firm
being able to default on bank loans when it is still solvent. At the same time, a
defaulting firm faces the prospect of being punished if it is caught. This punishment
involves the confiscation of some fraction of a firm’s capital output, where the size of
this fraction depends on the quality of legal institutions. Given limited enforcement,
an entrepreneur may decide to default even though its solvent. The results of the paper
emphasise the role that limited enforcement plays in determining the default risk and
access to funding by small firms.
The growth of firms depends on the level of access to external financing which
in turn depends largely on the informational asymmetries and the contractual ar-
rangements between investors and entrepreneurs. In a dynamic general equilibrium
framework, Amaral and Quintin (2010) find that the average scale of production in-
creases with the quality of enforcement and that the importance of limited enforcement
rises with the importance of capital in production2. Whilst imperfect information cre-
ates uncertainty about the default risk of borrowers, limited enforceability of financial
contracts reflects how much lenders loose in the event that borrowers default.
The above analysis yields interesting insights although one issue that is not looked
at is the effect of limited enforcement on firm funding and default risk. Costly contract
enforcement means that lenders will receive less compensation when firms default which
will impact on default risk. In turn, this will alter contract arrangements and vice versa.
Imperfect information can have important implications for borrowing and lending,
especially when there is limited enforcement of contracts.
Limited enforceability of contracts is especially important for new and smaller
firms who face working capital constraints and collateral problems which mean that
1Limited contract enforcement refers to the difficulty with which lenders can recover defaulted loans.Also, the World Bank have likened (limited) contract enforcement to the time and cost for resolvingcommercial dispute through courts.
2That is to say bad enforcement results in self-financing of production and on a small scale.
78
they rely mostly on external (as opposed to internal) financing. This has implications
not only for the growth of small firms but also for aggregate growth and welfare. It
is argued by Albuquerque and Hopenhayn (2000) that strong enforceability can help
explain the growth of small and new firms. Amaral and Quintin (2010) find that weak
enforceability has a negative effect on small firms’ access to finance, arguing that such
firms are forced to rely mainly on self-funding and to operate on a small scale because
of credit constraints which deny them of external funding. Additionally, Steinberg
(2013) argued that in countries with imperfect financial markets, productive firms are
mostly financially constrained. As a result, firms are impaired from borrowing enough
to reach their optimal sizes.
In spite of the above, little research has been conducted–especially within the
context of a DSGE framework–on exploring the interlinkages between limited contract
enforcement, asymmetric information, financial intermediation and firm funding. The
present paper seeks to do this. In particular, we study the implications of limited
enforcement for financial intermediation, small firm funding, economic growth and
welfare in a DSGE framework. We do this by modifying the models of Carlstrom and
Fuerst (1997) to allow for the imperfect enforcement on loan contracts. In doing so,
we draw upon the works of Khan and Ravikumar (2001), Marcet and Marimon (1992),
Castro et al. (2004), Quintin (2000), Cooley et al. (2003), Boedo et al. (2011), Bernanke
et al. (1999), De Fiore et al. (2011), and Amaral and Quintin (2010). Our work relates
with Cooley et al. (2003) on the assumption that firms which default in one period
are not excluded from the financial market in subsequent periods. We make the same
assumption, but also assume that firms can use funds from defaulting in next period
production. Marcet and Marimon (1992) argue that better investor protection in the
form of better contract enforcement leads to better risk sharing which creates a greater
supply of loanable funds. This results in a greater demand for capital which leads
to a higher interest rate but which also raises the income of households; at the same
time, there is a reduction in entrepreneurs’ income, a reduction in current savings and
79
a reduction in next period capital3. Their central conclusion is that better contract
enforcement results in less growth. We challenge this conclusion by arguing that better
contract enforcement helps in the transfer of resources to lenders (households) which
is accessed via banks by small firms to finance investment projects.
We show that business cycle fluctuations and the volatility of output are affected
by the degree of limited contract enforcement. Specifically, we establish that limited
enforcement amplifies the effects of shocks on the economy. We also find that limited
enforcement coupled with the ability of firms to default when solvent creates a problem
for the establishment and growth of smaller firms as a result of over accumulation of
internal funds by larger firms. Finally, given that firms are able to default when
solvent, and that households provide loanable funds, we also demonstrate that limited
enforcement is associated with welfare loss to households.
As indicated earlier, our work follows Bernanke et al. (1999), De Fiore et al.
(2011), Carlstrom and Fuerst (1998, 2001), and Carlstrom et al. (2010) on asymmetric
information in financial markets. To engage in investment opportunities, risk neutral
entrepreneurs have the potential to access funds from lenders. However, this funding
is constrained because of the agency costs involved. Lenders are risk averse households
who offer loans to entrepreneurs through the Capital Market Fund (CMF)/Bank. A
key feature of our model is the distinction between the monitoring cost and enforcement
cost, in the event that an entrepreneur defaults on its loan. We show how a high degree
of limited enforcement results in a loss of welfare to households and the economy in
general. We find that a high degree of limited contract enforcement reduces the supply
of funds and impedes small firms’ access to working capital which has implications for
the growth of the economy. We establish that the probability of default, risk premium
and the resulting cost of borrowing increase monotonically with the degree of limited
contract enforcement. We also show that the effects of both aggregate productivity and
wealth transfer shocks are amplified by an increase in the degree of limited contract
enforcement.
3A supply side effect works through the demand effect. When the supply side effect is stronger, thestricter the restrictions on capital flows (Castro et al. (2004)).
80
As a motivation for our theoretical analysis, we first conduct an empirical in-
vestigation into the effect of limited enforcement and poor depth of credit information
on output. Depth of credit information in our empirical work relates closely to the
monitoring cost in our theoretical model. In a similar vein, limited enforcement in our
empirical work proxies for the degree of limited enforcement in our theoretical model,
which pertains to the “cost” that lenders have to incur (through the legal system e.g.
legal fees) in order to recover any “hidden capital from defaulting firms. Using data on
a broad sample of countries, we find that limited enforcement affects output negatively.
Also, we find that poor credit information has negative impact on output. This results
are robust to various sensitivity tests.
The rest of the paper is organised as follows. In Section (3.2), we present the
empirical analysis of the effect of limited enforcement on output. In Section (3.3), we
set out the theoretical model that we use to study the relationship between firm funding
and limited enforcement of contracts and provide the solution. We then calibrate the
model and present our findings. In Section (3.4), we make some concluding remarks.
3.2 Empirical Observations
As a prelude to our theoretical analysis, we first conduct an empirical investigation
into the relationship between financial contract enforcement and aggregate economic
activity. Specifically, we seek to obtain evidence about the extent to which limited
enforcement4 has influence on both the level and volatility of output either directly
or indirectly. The literature on contract enforcement have stressed it importance in
economic growth (see Monge-Naranjo (2009); Steinberg (2013)). Using data on credit
information and enforcement costs, Steinberg (2013) finds that the latter exacerbates
the effects of poor depth of credit information on total factor productivity. Addition-
ally, their finding is consistent with other studies on the effect of credit bureaus and
borrowers’ information on access to credit, in countries with limited contract enforce-
4 We use a measure of limited enforcement different than the one used by Cooley et al. (2003).
81
ment (see Djankov et al. (2007); Jappelli and Pagano (2002); Brown et al. (2009)).
Further to this, Monge-Naranjo (2009) finds countries where the legal system gives
priority to creditors to have better-developed banks and improved private sector credit
as a ratio of GDP, than countries where laws do not give a high priority to creditors.
3.2.1 Data and Methodology
We use data from the World Bank’s Development Indicators and the World Bank’s
Doing Business Index from 2004 to 2012 for a sample of 57 countries (including both
developed and developing countries). A list of these countries is given in Appendix
(3.6). Our measure of output is logarithm of real GDP, whilst we proxy for imperfect
contract enforcement using the contract enforcement cost index. Djankov et al. (2002)
developed the methodology used by the World Bank for constructing the contract
enforcement cost index. Typically, the index captures the cost, as a fraction of the
claim (total amount of loans defaulted upon), that a lender (complainant) may incur
in order to enforce a contract. Accordingly, therefore, a higher value of this index
means that contracts will be more costly to enforce. A higher value of the contract
enforcement measure means that enforcement is more costly. For present purposes,
we convert this to the fraction of defaulted debt recovered by lenders after default is
announced. An increase in the value of this is then understood to mean an improvement
in contract enforcement.
As an additional measure of financial market imperfections, we also include the
depth of credit information (improvements in which are indicated on a scale from 0
to 6). The methodology used by the World Bank to construct the depth of credit
index was developed by Djankov et al. (2007). This index measures the coverage,
scope and accessibility of information about the credit histories of individuals and
firms. Depth of credit information could be related to monitoring and verification cost
in our theoretical model. Accordingly, bad depth of credit information implies high
monitoring and verification cost and low output, in the theoretical model (see Table
(3.3.3.5)). Table (3.6.1.3) reports the summary statistics of these variables. Depth
82
of credit information is the most volatile variable followed by output and contract
enforcement. This implies volatility of 2.048, 1.031 and 0.395, respectively.
Figure (3.2.1.1) presents the scatter plots of output, contract enforcement and
depth of credit information. Figure (3.2.1.1) shows that output is positively correlated
with both contract enforcement and credit information.
91
01
11
21
3lo
g(re
alG
DP
)
−.5 0 .5 1Contract Enforcement
91
01
11
21
3lo
g(re
alG
DP
)
0 2 4 6Credit information
Figure 3.2.1.1.: Scatter Plot of Real GDP, Credit Information and ContractEnforcement
Figure (3.2.1.2) presents the scatter plots of output volatility and contract enforcement.
Figure (3.2.1.2) shows that the volatility of output is negatively correlated with contract
enforcement.
83
.05
.1.1
5.2
.25
.3S
tan
da
rd D
evia
tio
n o
f G
DP
)
−.5 0 .5 1Contract Enforcement
Figure 3.2.1.2.: Scatter: Standard Deviation of GDP and Contract Enforcement
The foregoing casual inspection of the data is supplemented with an economet-
ric investigation in which we estimate the following equation adopted from Steinberg
(2013):
logRealGDPit =
γ + α1CONENFit + α2CREINFOit+
α3CONENF ∗ CREINFOit + ηi + µt + εit
where i is the country index and t is time. The dependent variable is the logarithm of
real GDP. The variable CONENFit measures the amount of debt recovered through
contract enforcement after default by firms. In other words it shows how much investors
are able to recoup, through the legal system, from firms that declare bankruptcy. The
84
variable CREINFOit denotes the depth of credit information. The credit inform-
ation of a country is ascertained from data on firms, individuals, utility companies
and financial institutions in the form of their credit history which is available to all
parties. CONENF ∗ CREINFOit, is the interaction between contract enforcement
and credit information. The intuition behind this interaction term is to capture the
effect of contract enforcement on output given credit information or the effect of credit
information on output given the degree of contract enforcement. By doing this we are
able to mimic the outcome of the interaction between the monitoring/verification cost
parameter (which proxies depth of credit information) and the limited enforcement
parameter in our theoretical model. The country and time fixed effects are ηi and µt
respectively while εit is the error term. The model is estimated in Stata and the code
is provided in Appendix (A.2).
3.2.2 Results
The results of the estimation are presented in this section. We use both fixed effects
(FE) and random effects (RE). There are no significant differences between the FE
and RE estimates. Given this, we prefer the random effect specification because it is
more efficient. The results in Table (3.6.1.4) are for both time and country FE and
RE. The coefficient on contract enforcement has the expected (positive) sign and is
significant at 1% in all specifications (columns). The coefficients from the RE models
are, however, larger than the FE models. Similarly, the depth of credit information
has the expected (positive) sign and significant at 1% as well. The coefficient on the
interaction term is negative and significant at 5%.
Table (3.6.1.5) displays the results for country FE and RE. Consistent with the
results in Table (3.6.1.4), we find that the coefficients on contract enforcement and
depth of credit information have positive sign and significant at 1% in all specifications.
Again, we find that the coefficients from the RE models are, however, larger than the
FE models. Additionally, we observe that, generally, the country effects models have
larger coefficients than the time and country effects models. Finally, the coefficient
85
on the interaction term is negative and significant at 1% in the country FE and RE
models.
The results in Table (3.6.1.6) are for both time and country FE and RE for sub-
sample of 34 countries. Table (3.6.1.6) (see in appendix (3.6)) report the results for
a sub-sample of 34 countries which display most variation in their time series data.
Consistent with the results in Table (3.6.1.4), we find that the coefficients on contract
enforcement have positive sign and significant at 1% in all specifications. Depth of
credit information has positive and significant coefficients in all specifications except
in column 8 in Table (3.6.1.6). We find that the coefficients from the RE models are,
however, larger than the FE models. Surprisingly too, the coefficient on the interaction
term is negative and insignificant.
Table (3.6.1.7) displays the results for country FE and RE for sub-sample of 34
countries. We find that the coefficients on contract enforcement and depth of credit
information have positive sign and significant at 1% in all specifications. We find that
the coefficients from the RE models are, however, larger than the FE models. Also, we
observe that, generally, the country effects models have larger coefficients than the time
and country effects models. Contrary to the results in Table (3.6.1.6), the coefficient
on the interaction term is negative and significant at 1% in the country FE and RE
models in Table (3.6.1.7).
The positive and significant coefficient on contract enforcement indicates that
output increases when the cost of contract enforcement is low meaning that investors
are able to recoup a larger amount of debt when firms default. Similarly, the positive
and significant coefficient on the depth of credit information implies that when credit
information on borrowers is more available, investors are more capable of identifying
firms with good prospects and allocating loans towards these firms. In sum, the coeffi-
cients on contract enforcement and the depth of credit information indicate that both
measures of financial development are positively related to output. The negative and
significant coefficient on the interaction term means that, given an economy with weak
contract enforcement, a deterioration of the existing level of credit information is likely
86
to dampen the fall in output (or alternatively, given low depth of credit information,
a deterioration in contract enforcement is likely to dampen the fall in output). In
other words, the effect of contract enforcement on output is smaller when the depth of
credit information is higher (or alternatively, when contract enforcement is higher the
effect of depth of credit information on output is smaller) and vice versa. Either way,
the result suggests that different types of financial market imperfection tend to show
negative synergy between them–they are inhibiting each other.
Our result also indicates that the effect of contract enforcement on output depends
on credit information, which is consistent with the prediction of our theoretical model
(see Table (3.3.3.5)). Table (3.3.3.5) also shows that output increases with better
credit information (lower monitoring cost) and better contract enforcement (lower cost
of enforcement).
3.3 The Investment Model
The model is based on Carlstrom and Fuerst (1997), extended to allow for imperfect
contract enforcement. The model economy consists of a continuum of agents of unit
mass, a fraction (1 − η) of which are risk averse households and a fraction η are risk
neutral entrepreneurs (or capital producing firms). Households who own (shares in) the
consumption-good producing firms also supply labour and rent capital to these firms,
invest in capital and advance intra-period loans via Capital Market Fund (CMF)/Bank
to entrepreneurs. Entrepreneurs produce capital goods using net worth and external
funds in the form of loans from the CMF/Bank.
3.3.1 The Financial Contract
In this section we discuss the financial contract in a partial equilibrium setting. It is
one period in length, negotiated at the beginning of the period and resolved by the
end of the same period. The contract involves the entrepreneur and the lender both of
87
which are risk neutral5. The lender has resources that he can lend to entrepreneur with
some positive net worth. Each entrepreneur is endowed with a stochastic technology
that transforms i consumption goods into ωi units of capital, where ω is idiosyncratic
technology shock. The shock ω, is i.i.d. across time and across entrepreneurs, with cu-
mulative distribution function Φ and probability density function φ. We assume ω has
mean E[ω] = 1, standard deviation σω, and is privately observed by the entrepreneur,
but others can privately observe ω only after paying the monitoring cost of µi capital
units. The monitoring cost denominated in terms of capital is proportional to i and
independent of the realisation of ω. To ensure that the asymmetric information in the
model is important, we assume that net worth is sufficiently small so that entrepreneurs
would like to receive some external financing to finance investment. Otherwise, entre-
preneurs would not need to borrow to finance investment. To finance the investment
i, the entrepreneur uses its net worth n and borrows (i − n) consumption goods and
agrees to repay (1 + rk)(i−n) capital goods to the lender, where rk is the lending rate.
Entrepreneur defaults at the end of the period if the realisation of ω is low. However,
if the entrepreneur defaults, it can “hide” a fraction ζ of the capital. The inability of
lenders to recover this “hidden” capital due to weakness in legal institutions is what
we refer to as limited contract enforcement. While monitoring cost (µi capital units)
pertains to the cost of monitoring borrowers, limited enforcement involves the “cost”
that lenders have to incur (which is equivalent to volume of this “hidden” capital) in
order to recover the “hidden capital. Therefore, if the entrepreneur does not default,
it receives:
ωi− (1 + rk)(i− n) (3.3.1.1)
5 In the general equilibrium setting, risk-averse households are the source of loanable funds to
entrepreneurs. However, in terms of the financial contract, they will be effectively risk neutral
because (1) there will be no aggregate uncertainty over the duration of the contract and (2)
households can diversify away all idiosyncratic risk.
88
capital goods, which it can then sell at the price q (the price of aggregate capital). If
the entrepreneur defaults, however, it receives:
ζωi (3.3.1.2)
Comparing Equations (3.3.1.1) and (3.3.1.2), the entrepreneur will default if and only
if
(1− ζ)ωi < (1 + rk)(i− n)
This is equivalent to Carlstrom and Fuerst (1997) when ζ = 0.
It is then possible to define a default threshold ω such that the entrepreneur will
default for ω < ω and not default for ω ≥ ω. This threshold is determined by:
(1− ζ)ωi = (1 + rk)(i− n) (3.3.1.3)
If ω ≥ ω, the entrepreneur does not default and he receives ωi − (1 + rk)(i − n). If
ω < ω, the entrepreneur defaults and he receives ζωi. In both cases, the entrepreneur
can then sell the capital it has at the price q. Therefore, expected entrepreneurial
income is given by
q
[∫ ω
0
ζωidΦ(ω) +
∫ ∞ω
[ωi− (1 + rk)(i− n)
]dΦ(ω)
]Using Equation (3.3.1.3) to substitute for (1 + rk)(i− n), this becomes:
qi
[ζ
∫ ω
0
ωdΦ(ω) +
∫ ∞ω
ωdΦ(ω)− (1− ζ)ω(1− Φ(ω))
]
Therefore, as a result of this contract, the entrepreneur expects to receive qif(ω), where
f(ω) is the the fraction of the expected capital output received by the entrepreneur.
This is defined to be:
89
f(ω) = 1− (1− ζ)
[∫ ω
0
ωdΦ(ω) + ω(1− Φ(ω))
](3.3.1.4)
Similarly, for the lender, if ω ≥ ω, the entrepreneur does not default and the
lender receives (1 + rk)(i − n) in capital units. If ω < ω, the entrepreneur defaults
and the lender receives ((1− ζ)ω−µ)i capital units. Then expected lender’s income is
given by
q
[∫ ω
0
((1− ζ)ω − µ)idΦ(ω) +
∫ ∞ω
(1 + rk)(i− n)dΦ(ω)
]
Again, using Equation (3.3.1.3), the expected lender’s income simplifies to
qi
[(1− ζ)
{∫ ω
0
ωdΦ(ω) + ω(1− Φ(ω))
}− µΦ(ω)
]
As a result of this contract, the lender expects to receive qig(ω), where g(ω) is
the fraction of the expected capital output received by the lender. This is defined to
be:
g(ω) = (1− ζ)
[∫ ω
0
ωdΦ(ω) + ω(1− Φ(ω))
]− µΦ(ω) (3.3.1.5)
Moreover, using Equations (3.3.1.4) and (3.3.1.5) we arrive at
f(ω) + g(ω) = 1− µΦ(ω) (3.3.1.6)
This implies that, on average, monitoring results in the destruction of some of the pro-
duced capital, and the remainder of this capital is then split between the entrepreneur
and the lender.
The optimal contract is given by the pair (i, ω) (taking as given net worth n and
capital price q) which solves:
maxi, ω
qif(ω)
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subject to
qig(ω) ≥ i− n Lender’s Participation constraint
qif(ω) ≥ n Entrepreneur’s Participation constraint, which is always satisfied
The solution6 to the optimal contract is the following:
q
[1− µΦ(ω)− µφ(ω)f(ω)
(1− ζ)(1− Φ(ω))
]= 1 (3.3.1.7)
This can also be written as:
q
[1− µΦ(ω) + µφ(ω)
f(ω)
f ′(ω)
]= 1
This implicitly defines a function ω(q). Then, given ω(q), we can solve for optimal
investment using the participation constraint of the lender:
i(q, n) =n
1− qg(ω(q))(3.3.1.8)
Substituting in ω(q), this gives us the function i(q, n), which represents the optimal
amount of consumption goods placed into the capital-producing technology (given q
and net worth n). Expected capital output is then given by:
Is(q, n) ≡ i(q, n) [1− µΦ(ω(q))]
This can be interpreted as the investment supply function. This implies that the
supply function of entrepreneurs aggregates. Aggregate investment depends only on
the economy-wide price of capital q and aggregate net worth. It can then be shown
that ∂Is/∂q > 0 and ∂Is/∂n > 0.
An entrepreneur who receives loan of one unit of consumption good from house-
hold (via CMF/bank) expects to make a risky return of q(1 + rk) consumption good
6See Appendix (3.5.4) for detailed derivation.
91
at the end of the investment period. Therefore, the risk premium of the model is
q(1 + rk)− 1. Substituting for (1 + rk) using Equation (3.3.1.3), the risk premium can
also be written as:
q(1 + rk)− 1 = q(1− ζ)ωi
i− n− 1
Finally, we may define leverage z, of the entrepreneur as the ratio of external
funding (i− n) to net worth n of the entrepreneur. This is given by
z =i− nn
Then using Equation (3.3.1.8) this can be re-written as:
z =qg(ω(q))
1− qg(ω(q))
3.3.2 The General Equilibrium Model
We now embed the contracting problem into a standard RBC model. We further
assume that, using consumption goods, new capital is created at the end of the period
with a non-stochastic one-to-one transformation rate. The newly produced capital is
then utilised in the next period. We use the same timing in this model. The one-
to-one transformation assumption is replaced with the contracting problem so that a
household who wants to purchase capital, must first fund the production of capital (an
entrepreneurial project), which is subject to agency problems.
The economy consists of a continuum of agents of unit mass, a fraction (1 − η)
of which are households and a fraction η are entrepreneurs. Firms produce the single
consumption good, but it is assumed that these consumption-producing firms are not
subject to any agency problems.
92
3.3.2.1 Households
Households are infinitely lived, with preferences:
E0
[∞∑t=0
βtU(ct, 1− Lt)
]
where U(ct, 1 − Lt) = ln(ct) + ν(1 − Lt) is the instantaneous utility function, E is
the expectation operator conditional on period 0 information, β ∈ (0, 1) is the dis-
count factor, ct is household consumption, Lt is labour. Households supply labour to
consumption-producing firms at wage rate wt, rent their accumulated capital holdings
to consumption-producing firms at rental rate rt, purchase consumption from these
firms at the price 1 (note that consumption is the numeraire), and purchase new cap-
ital goods at a price of qt. Within the period, households also lend to entrepreneurs
(through the CMF/Bank) to help finance the production of capital. Households who
own (shares in) the consumption-good producing firms then purchase capital goods at
the end of the period with the assistance of CMF/Bank.
The budget constraint faced by the household is then:
ct + qt[kht+1 − (1− δ)kht
]= wtLt + rtk
ht
where kht is the stock of capital owned by the representative household. The profits of
the CMF/bank are not included here, because they will be zero.
Optimal consumption-labour decision is determined by the following:
wt =UL(ct, 1− Lt)Uc(ct, 1− Lt)
Also, optimal7 household consumption-investment decision is determined by the fol-
lowing:
qtUc(ct, 1− Lt) = βEt {Uc(ct+1, 1− Lt+1) [qt+1(1− δ) + rt+1]}
7See Appendix (3.5.1) for detailed derivation.
93
3.3.2.2 Consumption-good Producing Firms
There are a continuum of consumption-producing firms in the economy who utilise a
standard production function8 with Constant Returns to Scale (CRS) specified as:
Yt = AtF (Kt, Ht, Het )
where Yt is aggregate output of the consumption good, Kt is the aggregate capital
stock (including entrepreneurial capital), Ht is aggregate supply of household labour,
and Het is the aggregate supply of entrepreneurial labour. At is stochastic aggregate
productivity and evolves according to log(At) = (1− ρA)A + ρA log(At−1) + εt, where
εt is a serially uncorrelated, i.i.d. and normally distributed shock; and ρA is the auto-
correlation coefficient. This consumption-good producing technology is assumed to
be Cobb-Douglas (details to be discussed in Section (3.3.3)). Perfect competition in
factor markets ensures that factor prices are equal to their respective marginal products:
rt = AtF1(Kt, Ht, Het ), wt = AtF2(Kt, Ht, H
et ), and wet = AtF3(Kt, Ht, H
et ), where wet is
the wage rate for entrepreneurial labour. As explained in Carlstrom and Fuerst (1997),
the assumption of entrepreneurial labour income is to ensure that each entrepreneur
has a non-zero level of net worth. This is because the financial contracting problem
will not be well defined for any zero levels of net worth.
3.3.2.3 Entrepreneurs
Entrepreneurs are long-lived and risk-neutral. Without any restrictions, entrepreneurs
will want to accumulate enough capital so that they are completely self-financed and
avoid agency costs by postponing consumption. To prevent this, we follow on Carlstrom
and Fuerst (1997) and assume that entrepreneurs discount the future more heavily
than households9. Following the risk neutrality assumption, entrepreneurs maximise
8We specify the production function as Yt = AtKαKt HαH
t Heαet
9In the earlier working paper version of their paper, Carlstrom and Fuerst (1997) assumed that aconstant fraction of the entrepreneurs died each period, and sold their accumulated capital stockto households. In terms of consumption, this is equivalent to assuming that the entrepreneursconsume a constant fraction of their capital holdings each period.
94
the following objective function:
E0
[∞∑t=0
(βγ)tcet
](3.3.2.1)
where cet is entrepreneurial consumption, and γ ∈ (0, 1) denotes the additional rate
of discounting for entrepreneurs to ensure that βγ < β. At the beginning of the
period the entrepreneur rents his previously accumulated capital and also inelastically
supplies labour, which we assume to be unity, to consumption good producing firms.
The entrepreneur then sells his remaining un-depreciated capital to households for
consumption goods. The net worth of the entrepreneur (in terms of consumption) at
the end of the transactions period is given by:
nt = wet + ket [qt(1− δ) + rt]
where ket refers to the capital holdings of the individual entrepreneur at the beginning
of the period. To undertake investment, the entrepreneur uses this net worth to form
the basis for any loan agreement that he will enter into with the lender. Risk neutrality
and the high internal return ensures the entrepreneur pours his entire net worth into the
capital-producing technology and borrows from the household (via the CMF/Bank).
Given the financial contract from Section (3.3.1), the entrepreneur chooses it = i(qt, nt),
where i(q, n) is defined in Equation (3.3.1.8). There is also an associated cutoff ωt =
ω(qt), where ω(q) is implicitly defined by Equation (3.3.1.7), given this investment. Let
xt denote the realised payoff (in terms of capital) to the entrepreneur given by:
x =
ωi− (1 + rk)(i− n) = ωi− (1− ζ)ωi = (ω − (1− ζ)ω)i if ω ≥ ω
ζωi if ω < ω
Then, given x, the entrepreneur makes the consumption decision:
cet + qtket+1 = qtxt
95
Let cet denote average entrepreneurial consumption. Then ηcet is aggregate entrepren-
eurial consumption. Aggregating across the budget constraints of all entrepreneurs, we
get:
ηcet + qtKet+1 = qt
Nt
1− qtg(ω(qt))f(ω(qt))
where Ket+1 is aggregate entrepreneurial capital stock and Nt is aggregate entrepren-
eurial net worth. Aggregate net worth is Nt = ηwet +Ket (qt(1− δ) + rt). Re-arranging,
tomorrow’s aggregate entrepreneurial capital stock (Ket+1) is given by:
Ket+1 = [ηwet +Ke
t (qt(1− δ) + rt)]f(ω(qt))
1− qtg(ω(qt))− ηcet
qt(3.3.2.2)
Dividing through by η (the mass of entrepreneurs), we get:
ket+1 = ntf(ω(qt))
1− qtg(ω(qt))− cetqt
where nt = wet + ket [qt(1− δ) + rt] is average entrepreneurial net worth and ket = Ket /η
is the average stock of capital owned by entrepreneurs.
Maximising the entrepreneur’s utility in Equation (3.3.2.1) subject to the aggregate
entrepreneurial capital stock in Equation (3.3.2.2) (see Appendix (3.5.3) for detailed
derivation) gives the entrepreneur’s Euler equation:
qt = βγEt{
[qt+1(1− δ) + rt+1]qt+1f(ωt+1)
1− qt+1g(ωt+1)
}
The first term (in brackets) represents the market return on capital whilst the second
term denotes the additional return on internal funds.
96
3.3.2.4 Capital Market Fund (CMF)/Bank
The CMF/Bank lends (it(qt, nt)−nt) consumption goods to each entrepreneur with net
worth nt (measured in consumption units). Let Nt denote aggregate entrepreneurial
net worth. Since the investment function in Equation (3.3.1.8) is linear in net worth,
aggregate lending is(
qtg(ω(qt))1−qtg(ω(qt))
)Nt, denominated in terms of consumption units.
At the end of the period, ω is realised for all firms and the expected proceeds from
each individual entrepreneur is qti(qt, nt)g(ω(qt)). Given that i(qt, nt) is linear in nt, this
aggregates. Therefore, the total proceeds to the CMF/Bank are Nt1−qtg(ω(qt))
qtg(ω(qt)).
Comparing aggregate lending to total proceeds of the CMF/Bank, its profits are zero.
This is because, in the optimal contracting problem, the lender’s participation con-
straint holds with equality.
3.3.2.5 Market Clearing Conditions
We close the model with the market-clearing conditions. The economy is characterised
by four markets: two labour markets, a consumption-goods market, and a capital goods
market. Labour market clearing for the consumption-goods sector ensures:
Ht = (1− η)Lt
Het = η
Consumption-good market clearing implies:
(1− η)ct + ηcet + ηit = Yt
where ct is the representative household’s consumption, cet is average entrepreneurial
consumption, and it is average entrepreneurial investment. Finally, the capital goods
market clearing implies:
97
Kt+1 = (1− δ)Kt + ηit [1− µΦ(ωt)]
where aggregate capital Kt = (1− η)kht + ηket includes both household and entrepren-
eurial capital.
3.3.2.6 Recursive Competitive Equilibrium
A recursive competitive equilibrium consists of the following decision rules: kht+1, ket+1,
Kt+1, Ket+1, qt, nt, it, ωt, c
et , ct, rt, wt, w
et , Ht, H
et , Lt, and Yt, such that these decision rules
are stationary functions of (Kt, Ket , At) and the following conditions are satisfied:
(1) Optimality conditions for household labour supply:
UL(ct, 1− Lt)Uc(ct, 1− Lt)
= wt
(2) Optimality conditions for household investment:
qtUc(ct, 1− Lt) = βEtUc(ct+1, 1− Lt+1) [qt+1(1− δ) + rt+1]
(3) Market clearing for capital good market:
Kt+1 = (1− δ)Kt + ηit [1− µΦ(ωt)]
(4) Market clearing for consumption:
(1− η)ct + ηcet + ηit = Yt
(5) First Order Conditions defining ωt = ω(qt):
qt
[1− µΦ(ωt) + µφ(ωt)
f(ωt)
f ′(ωt)
]= 1
(6) Average investment it set optimally (given average net worth nt):
98
it = i(qt, nt) =nt
1− qtg(ωt)
(7) Average entrepreneurial net worth nt:
nt = wet + ket [qt(1− δ) + rt]
(8) Next period’s average entrepreneurial capital ket+1:
ket+1 = ntf(ωt)
1− qtg(ωt)− cetqt
(9) Next period’s aggregate entrepreneurial capital Ket+1:
Ket+1 = [ηwet +Ke
t (qt(1− δ) + rt)]f(ω(qt))
1− qtg(ω(qt))− ηcet
qt
(10) First Order Conditions for entrepreneurial consumption:
qt = βγEt{
[qt+1(1− δ) + rt+1]qt+1f(ωt+1)
1− qt+1g(ωt+1)
}(11) Aggregate capital:
Kt+1 = (1− η)kht+1 + ηket+1
(12) Labour market clearing for the consumption-goods sector:
Ht = (1− η)Lt
Het = η
(13) Factor markets:
99
rt = AtF1(Kt, Ht, Het )
wt = AtF2(Kt, Ht, Het )
wet = AtF3(Kt, Ht, Het )
3.3.3 Calibration and Results
We simulate and solve the model in Dynare (see Appendix (A.2) for details). To
simulate the model, we first need to calibrate it. The calibration is at the non-stochastic
steady state. As noted earlier, we assume that utility is logarithmic in consumption
and linear in leisure. Following Carlstrom and Fuerst (1997), we choose ν, disutility
of labour supply parameter, to be 2.52 so that L = 0.3. We normalise η, fraction of
entrepreneurs, to be 10%.
The Cobb-Douglas consumption-good producing technology has 36% as share of
capital and 63.99% as share of household labour. Drawing on Carlstrom and Fuerst
(1997) and Carlstrom and Fuerst (1998), we set as 0.01% the share of entrepreneurial
labour. As stated earlier, this is also to, purposely, ensure that each entrepreneur always
has positive level of net worth. The autocorrelation coefficient ρA of the stochastic
aggregate productivity is set to 0.95 following standard RBC calibration. The non-
stochastic steady state value of aggregate productivity A is set to 1 while we set the
standard deviation of the innovation to aggregate productivity shock to σA = 1%.
In order to understand the impact of wealth redistribution in the economy, we
consider a one-time shock to the distribution of wealth in the form of transfer of
capital from entrepreneurs to households (lenders). To do this, we restate the net
worth equation in the model bloc as nt = wet + ket [qt(1− δ) + rt] − σnεn,t, where εn,t
is a serially uncorrelated shock to the redistribution of wealth, and σn is the standard
deviation of this shock.
There is enormous controversy over the verification cost parameter µ (see Carl-
strom and Fuerst (1997, 1998, 2001); Levin et al. (2004); De Fiore et al. (2011)) but
100
we set it to 0.15.
The distribution of the idiosyncratic productivity shock is i.i.d. and follows a
log-normal distribution, and as noted earlier, with mean 1 and standard deviation of
σω. Following Carlstrom and Fuerst (1997), we calibrate this standard deviation of the
distribution of the idiosyncratic productivity shock to σω = 20.7%, and the steady-
state additional discount rate for entrepreneurs to about γ = 91% so as to generate a
quarterly steady-state credit spread of about 0.5% and a quarterly bankruptcy rate of
about 1%. We also calibrate β (the discount factor of households) to 0.99 to match a
quarterly nominal interest rate of 1%.
Table 3.3.3.1.: Calibration
Description Parameter ValueContract Enforcement ζ (0,1)Verification Cost µ 0.15Discount Factor β 0.99Labour Supply Disutility ν 2.52Productivity Parameter A 1.00Persistence in Aggregate Technology Shock ρA 0.95Depreciation Rate of Capital δ 2%Share of Capital in Production αK 36%Share of Entrepreneurial Labour in Production αe 0.01%Share of Household Labour in Production αH 63.99%Additional Discount Rate for Entrepreneurs γ 91%Fraction of Entrepreneurs η 10%Standard Deviation of Φ(ω) σω 20.7%Standard Deviation of Net Worth Shock σn 10%Standard Deviation of Aggregate Productivity Shock σA 1%
The recovery rate, (1 − ζ), is the fraction of capital that the lenders are able
to recoup after a default is announced by the entrepreneurs. One presumes that this
would depend positively on the strength of contract enforcement as determined by
the quality of legal institutions. The better is the legal system the greater is the
enforceability of contracts, and the larger is the recovery rate. Following Steinberg
(2013), who calibrates the recovery rate to 23% for an average country with limited
enforcement, and the Doing Business index of World Bank (as used in Section (3.2)),
we look at three scenarios of limited enforcement in our analysis. We calibrate ζ to
101
70%, meaning a recovery rate, (1 − ζ), of 30% for an average country with limited
enforcement, ζ to 40%, indicating a recovery rate, (1 − ζ), of 60% for an average
country with moderately good enforcement, and ζ to 0 for an average country with
perfect enforcement. The case of ζ = 0 coincides with agency costs models with no
limited enforcement problems as in Carlstrom and Fuerst (1997) and Carlstrom and
Fuerst (1998).
3.3.3.1 Aggregate Technology Shocks
Figures (3.3.3.1) and (3.3.3.3) show the impulse responses to a 1% positive aggregate
technology shock for the baseline model, for three cases of limited enforcement (i.e.
ζ = 0% (perfect enforcement), ζ = 40% (limited enforcement) and ζ = 70% (imperfect
enforcement)). The positive productivity shock increases output, household consump-
tion and net worth on impact. The increase in output and net worth results in an
increased demand for capital which pushes the price of capital up. As the price of
capital rises, the demand for investment falls which dampens the initial increase in
output. As demand for investment falls, it boosts household consumption which in
turn reduces household labour supply and dampens the increase in output. Though
there is an increase in net worth, because the positive shock increases wages (including
entrepreneurial wages) and rental income, the high price of capital makes the initial
increase sluggish.
Increasing returns to entrepreneurial internal funds additionally increases net
worth as the risk-neutral entrepreneur takes advantage of the rising price of capital by
reducing their consumption. As the price of capital returns to its steady-state level,
net worth attains it maximum before returning to the steady state. The increasing
in demand for investment and value of net worth leads to an increase in demand for
external funds. This pushes up the default threshold and the probability of default on
impact of the shock. Following from the rise in the probability of default, lending rate
rises on impact of the shock.
102
0 10 20 301
1.01
1.02
1.03
Quarters
Output
0 10 20 301
1.005
1.01
1.015
Quarters
Households Consumption
0 10 20 300.998
1
1.002
1.004
1.006
Quarters
Household Labour
0 10 20 300.96
0.98
1
1.02
1.04
Quarters
Entrepreneurial Consumption
0 10 20 300.995
1
1.005
1.01
1.015
Quarters
Price of Capital
Agency Cost Only
ζ=40%
ζ=70%
0 10 20 301
1.05
1.1
Quarters
Entrepreneurial Capital
Figure 3.3.3.1.: Impulse responses from a positive technology shock. The vertical axismeasures percentage deviations from the steady state. The horizontal axis measurestime in quarters.
103
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.95
10
15
Ris
k p
rem
ium
(in
per
cen
t)
Zeta (ζ)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90
1
2
Lev
erag
e
Risk premium
Leverage
Figure 3.3.3.2.: Relationship between expected leverage, expected risk premium andlimited enforcement in response to productivity shocks.
Additionally, the increase in value of internal funds, profit and the resulting increase
in demand for external funds contributes to an increase in leverage.
The amplification effect of limited contract enforcement in the model is displayed
by the three different lines corresponding to the different cases of contract enforceability.
The growth in investment is dampened by limited enforcement. With higher degree of
limited enforcement, the risk premium and the probability of default are much more
sensitive to increases in borrowing. As displayed in Figure (3.3.3.2), increases in degree
of limited enforcement (ζ) results in an increase in the risk premium and a decrease in
leverage. Figure (3.3.3.4) also shows that the rate of investment falls with the degree
of limited enforcement.
104
0 10 20 301
1.05
1.1
1.15
Quarters
Investment
0 10 20 300.99
1
1.01
1.02
1.03
Quarters
Probability of Default
0 10 20 300.99
1
1.01
1.02
1.03
Quarters
Lending Rate
0 10 20 300.995
1
1.005
1.01
1.015
Quarters
Risk Premium
0 10 20 301
1.05
1.1
1.15
Quarters
Entrepreneurial Net Worth
0 10 20 300.9
1
1.1
1.2Leverage
Quarters
Agency Cost Only
ζ=40%
ζ=70%
Figure 3.3.3.3.: Impulse responses from a positive technology shock. The vertical axismeasures percentage deviations from the steady state. The horizontal axis measurestime in quarters.
105
Therefore, given a productivity shock, with higher degree of limited enforcement, it
is more difficult for entrepreneurs to use their net worth to expand investment (hence
the lower growth in investment in Figure (3.3.3.3)). Output responds to investment by
displaying higher growth when the degree of limited enforcement is at its lowest level.
When the degree of limited enforcement is at its highest level, the growth in output is
at its lowest level. This reaction of aggregate output to the shock is consistent with
the findings of Cooley et al. (2003) and Amaral and Quintin (2010). The negative
effect of the limited enforcement on investment amplifies the increases in household
consumption which in turn reduces household labour supply. The reduction in labour
input is highest when the degree of limited enforcement is highest.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.92.18
2.2
2.22
2.24
2.26
2.28
2.3
2.32
2.34
2.36
2.38
Zeta (ζ)
Inv
estm
ent
Investment
Figure 3.3.3.4.: Relationship between expected investment and limited enforcementin response to productivity shocks.
As limited enforcement worsens, the price of capital rises. This is as a result of
106
the rise in risk premium and a fall in the supply of capital resulting from the dampened
growth in investment. As a result of this rise in price of capital, both entrepreneurial
capital and net worth increase the most when the degree of limited enforcement is
highest. As earlier discussed, weak enforceability also exacerbates the effect of the
shock on the probability of default, the lending rate and leverage. On impact of the
shock, the probability of default rises by 2% when the degree of limited enforcement is
70% (i.e. when a firm can walk away with 70% of its output after default), 1% when
the degree of limited enforcement is 40% (i.e. when a firm can walk away with 40% of
its output after default) and 0.6% when there is “perfect” enforcement. The impact
of the probability of default is reflected in the lending rate rising by 1.6%, 0.5% and
0.2%, respectively, when the degree of limited enforcement is 70%, 40% and 0%. As
lending rate and net worth increase following an increase in the degree of enforcement,
external funding is reduced resulting in leverage being lowest when the degree of limited
enforcement is highest.
3.3.3.2 Shocks to Net Worth
Figures (3.3.3.5) and (3.3.3.7) display the impulse responses to a shock to net worth,
for three cases of limited enforcement (i.e. ζ = 0% (perfect enforcement), ζ = 40%
(limited enforcement) and ζ = 70% (imperfect enforcement)). This shock will be a one-
time transfer of capital from entrepreneurs to households (lenders). The redistribution
is 20% of the steady-state capital stock. This transfer increases household capital and
reduces entrepreneurial net worth. This reduction in entrepreneurial net worth raises
the demand for external financing and thus raising agency costs of investment. The
decrease in net worth reduces investment which in turn decreases the supply of capital,
therefore raising the equilibrium price of capital. This decrease in investment also
leads to higher household consumption which serves as an incentive for households to
decrease their labour input.
107
0 10 20 300.8
0.9
1
1.1
1.2
Quarters
Entrepreneurial Net Worth
0 10 20 300.96
0.98
1
1.02
Quarters
Output
0 10 20 300.995
1
1.005
1.01
1.015
Quarters
Households Consumption
0 10 20 300.985
0.99
0.995
1
1.005
Quarters
Household Labour
0 10 20 300.85
0.9
0.95
1
1.05
Quarters
Entrepreneurial Consumption
0 10 20 300.99
1
1.01
1.02
1.03 Price of Capital
Quarters
Agency Cost Only
ζ=40%
ζ=70%
Figure 3.3.3.5.: Impulse responses from a negative shock to net worth. The verticalaxis measures percentage deviations from the steady state. The horizontal axismeasures time in quarters.
108
The total impact is therefore a reduction in output. The decrease in value of net
worth and demand for investment and the subsequent increase in demand for external
funds increases the probability of default. Following the rise in the probability of
default, lending rate rises. Additionally, the fall in the value of internal funds leads to
an increase in demand for external funds which in turn contributes to an increase in
leverage.
The amplification effect of limited contract enforcement in the model is displayed
by the three different lines corresponding to the different cases of contract enforceability.
As earlier argued, higher degree of limited enforcement results in the risk premium and
the probability of default being more sensitive to increases in borrowing.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.95
10
15
Ris
k p
rem
ium
(in
per
cen
t)
Zeta (ζ)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90
1
2
Lev
erag
e
Risk premium
Leverage
Figure 3.3.3.6.: Relationship between expected leverage, expected risk premium andlimited enforcement in response to net worth shocks.
109
0 10 20 300.7
0.8
0.9
1
1.1
Quarters
Investment
0 10 20 300.98
1
1.02
1.04
1.06
Quarters
Probability of Default
0 10 20 300.98
1
1.02
1.04
Quarters
Lending Rate
0 10 20 300.99
1
1.01
1.02Risk Premium
Quarters
0 10 20 300.9
0.95
1
1.05
1.1 Entrepreneurial Capital
Quarters0 10 20 30
0.8
1
1.2
1.4
1.6Leverage
Quarters
Agency Cost Only
ζ=40%
ζ=70%
Figure 3.3.3.7.: Impulse responses from a negative shock to net worth. The verticalaxis measures percentage deviations from the steady state. The horizontal axismeasures time in quarters.
110
As displayed in Figure (3.3.3.2), increases in degree of limited enforcement (ζ) results
in an increase in the risk premium and a decrease in leverage. Figure (3.3.3.4) also
shows that the rate of investment falls with the degree of limited enforcement. A one-
time wealth transfer to households instantaneously reduces net worth. Therefore, given
a higher ζ, it is even much more difficult for entrepreneurs to use their net worth to
expand investment (hence the lower growth in investment in Figure (3.3.3.7)).
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.92.15
2.2
2.25
2.3
2.35
2.4
Zeta ( ζ )
Inv
estm
ent
Investment
Figure 3.3.3.8.: Relationship between expected investment and limited enforcementin response to net worth shocks.
Output is at its lowest when the the degree of limited enforcement is at its highest
level but highest when the degree of limited enforcement is lowest. The negative effect
of the limited enforcement on investment further amplifies the increase in household
consumption which in turn reduces household labour supply. The reduction in labour
input is highest when the degree of limited enforcement is highest. The negative impact
111
of limited enforcement on both household labour supply and investment results in the
effect of the shock on output being equally amplified. The fall in net worth, investment
and output results in entrepreneurial capital also falling and attaining its lowest level
when the degree of limited enforcement is highest.
As the degree of limited enforcement increases, the effect of the transfer on the
probability of default, the lending rate and the degree of leverage is amplified. For
instance, after the shock, the probability of default rises by 3.3% when the cost of en-
forcement is 70% (i.e. when a firm can walk away with 70% of its output after default),
2.5% when when the cost of enforcement is 40% (i.e. when a firm can walk away with
40% of its output after default) and 2.5% when there is “perfect” enforcement10.
The impact of the probability of default is reflected in the lending rate rising by 3%,
1.1% and 0.7%, respectively, when the degree of limited enforcement is 70%, 40% and
0%. As lending rate increases and net worth decreases following an increase in the
degree of limited enforcement, external funding is reduced resulting in the degree of
leverage being lowest when the degree of limited enforcement is highest.
3.3.3.3 Sensitivity Analysis: Limited Enforcement, Output and Net Worth
In Table (3.3.3.2), following a positive productivity shock, an increase in the degree of
limited enforcement, from 0% to 40%, is associated with a decrease in output volatility
from 2.37% to 2.20% whilst an increase in the degree of limited enforcement from 0% to
70%, is associated with a decrease in output volatility from 2.37% to 2.05%. Similarly,
expected output decreases as the degree of limited enforcement increases. In contrast,
we find that as the degree of limited enforcement increases, expected net worth and its
volatility follow similar trends. In a similar vein, expected lending rate and its volatility
increase with the degree of limited enforcement. Our results are consistent with other
studies (see Quintin (2000); Cooley et al. (2003)) which made similar findings on the
10In the second quarter, for instance, the probability of default is 1.9%, 1% and 0.6% when the costof enforcement is 70%, 40% and 0%, respectively.
112
impact of limited contract enforcement on output.
Table 3.3.3.2.: Productivity Shock
Cost of Enforcement 0% 40% 70% 0% 40% 70%Statistic Mean Volatility
Output 1.01 1.00 0.99 2.37% 2.20% 2.05%Net Worth 0.91 1.41 1.80 7.10% 10.36% 12.44%Lending Rate 0.47% 1.36% 6.22% 0.11% 0.30% 1.16%
We measure volatility by standard deviations expressed in percentages.
Table (3.3.3.3) presents our findings following a one-time wealth transfer from
entrepreneurs to households (lenders). One interesting finding in the data (see our em-
pirical findings in Section (3.2)) is that countries with more limited contract enforce-
ment tend to exhibit more volatility in output. Result from our model with one-time
wealth transfer is able to reproduce this observation. Whist expected output decreases,
volatility of output increases as the degree of limited enforcement increases. Similarly,
both expected net worth and its volatility increase as the degree of limited enforcement
increases. Things are not different when it comes to the lending rate. Expected lending
rate and its volatility increase as the degree of limited enforcement rises.
This result may be seen as being especially pertinent for the case of small firms
that use their net worth as collateral and rely largely on external finance for production.
New entrants and smaller firms may be credit constrained and find the cost of loans
expensive as the degree of limited enforcement increases. The result suggests that
limited contract enforcement may be particularly an issue for the growth of such firms
and, with this, the growth of the economy as a whole, as argued by Amaral and Quintin
(2010) and Albuquerque and Hopenhayn (2000).
3.3.3.4 Sensitivity Analysis: Welfare Consequences of Limited Contract
Enforcement
A very important issue worth commenting on is the effect of limited enforcement on
household welfare, the presumption being that weaker enforcement reduces welfare.
113
Table 3.3.3.3.: One-Time Wealth Transfer
Cost of Enforcement 0% 40% 70% 0% 40% 70%Statistic Mean Volatility
Output 1.01 1.00 0.99 2.28% 2.32% 2.19%Net Worth 0.91 1.41 1.80 18.49% 18.46% 18.92%Lending Rate 0.47% 1.36% 6.22% 0.36% 0.62% 1.87%
We measure volatility by standard deviations expressed in percentages.
Following Lucas (1987), we estimate welfare loss (consumption equivalent) as the per-
centage decrease in households consumption in the economy with perfect enforcement
which makes households indifferent between the economy with limited enforcement
and the economy perfect enforcement (see Appendix (3.5.5) for detailed derivation of
welfare loss). In the context of the present model, when enforceability is poor, invest-
ment responds positively. In light of this, in response to a positive productivity shock,
households consumption increases which results in household labour supply falling.
This leads to household welfare increasing accordingly. However, the initial increase in
welfare is dampened when enforcement worsens. The result displayed in Table (3.3.3.4)
provides an additional support for the effect of limited enforcement on household wel-
fare, when there is a positive productivity shock. The result shows that as the degree
of limited enforcement increases from 40% to 70%, the average household consumption
equivalent welfare loss increases from 0.86% to 1.84%.
Table 3.3.3.4.: Welfare loss
Cost of Enforcement 40% 70% 40% 70%Statistic productivity shock wealth transfer
Consumption Equivalentof Welfare Loss 0.86% 1.84% 0.9% 1.89%
Welfare consequences of productivity shock and one-time wealth transfer
In response to a one-time transfer of wealth from entrepreneurs to households,
consumption of the latter increases which then results in labour supply falling. This
leads to household welfare increasing, on impact of the shock. However, as the the
transfer is one-time the initial increase in welfare is short-lived. In Table (3.3.3.4) we
114
present the results of the impact of the wealth transfer on households. We show that as
the degree of limited enforcement increases from 40% to 70%, the average consumption
equivalent welfare loss increases from 0.9% to 1.89%.
3.3.3.5 Limited Enforcement, Monitoring Cost and Output
Table (3.3.3.5) displays the effect of changes in monitoring cost and the degree of
limited enforcement on output.
Table 3.3.3.5.: Effect of Limited Enforcement and Monitoring Cost on Output
Monitoring and Verification Cost
µ = 5% µ = 10% µ = 15% µ = 20% µ = 25%
Degree of Enforcement Percentage Change in Output
ζ = 0% 1.82% 1.71% 1.66% 1.62% 1.59%ζ = 40% 0.90% 0.89% 0.88% 0.88% 0.86%ζ = 70% −0.42% −0.19% −0.10% −0.04% 0.00%
Smaller µ means better credit information. Smaller ζ means better contract enforcement.
Percentage change in output relative to the steady state output when ζ = 70%
It is observed that as monitoring cost fall (i.e. as credit information improves),
its effect on output increases. Similarly, as enforcement improves, its impact on output
increases. This findings is consistent with our empirical result, particularly, where we
establish that both poor depth of credit information and limited enforcement have
negative effect on output.
3.4 Concluding Remarks
This paper has presented a dynamic stochastic general equilibrium model of asym-
metric information and limited contract enforcement in financial markets. The first
of these features–a fairly standard way of incorporating capital market frictions into
macroeconomic models–is reflected in the idea of costly state verification by finan-
cial intermediaries. The second feature–a much less standard way of capturing such
frictions–is reflected in the notion of institutional weaknesses in holding defaulters to
115
account. It is this second aspect on which our interest has been focused and in which
the contribution of the analysis is mainly found.
We have shown how limited contract enforcement may affect fluctuations in key
macroeconomic variables (e.g. output, employment and investment) through its impact
on key financial variables (e.g. interest rates, risk premium, default risk and leverage).
Our results are particularly relevant for developing countries, where institutions are
often weak, fragile and fragmented because of poor quality of governance. Our analysis
suggests that improving such quality has the potential to improve the prospects of such
countries.
116
3.5 Appendix A
3.5.1 Household Optimisation Problem
Households maximise expected life time utility
E0
[∞∑t=0
βtU(ct, (1− Lt))
]subject to
ct + qt[kht+1 − (1− δ)kht
]= wtLt + rtk
ht
where U(ct, (1− Lt)) = ln(ct) + ν(1− Lt)
Lagrange for the problem:
L = E0
[∞∑t=0
βt [ln(ct) + ν(1− Lt)]
]
+E0
[∞∑t=0
βt[λt(wtLt + rtk
ht − ct − qt(kht+1 − (1− δ)kht )
)]]First Order Conditions from household maximisation problem:
c : Uc(ct, 1− Lt)− λt = 0 (3.5.1.1)
kht+1 : −qtλt + βEt [λt+1 (rt+1 + qt+1(1− δ))] = 0 (3.5.1.2)
L : UL(ct, 1− Lt) + λtwt = 0 (3.5.1.3)
Equation (3.5.1.3) implies λt = νWt
Note that Uc(ct, 1− Lt) = c−1t ; UL(ct, 1− Lt) = −ν. Then
wt =UL(ct, 1− Lt)Uc(ct, 1− Lt)
=ν
c−1t
(3.5.1.4)
Equation (3.5.1.4) implies:
ct =
(ν
wt
)−1
=(wtν
)
117
Using Equations (3.5.1.1) and (3.5.1.2) we can write the Euler Equation as:
qtUc(ct, 1− Lt) = βEt [Uc(ct+1, 1− Lt+1) (rt+1 + qt+1(1− δ))] (3.5.1.5)
Equation (3.5.1.5) is then simplified as:
qtc−1t = βEt
[c−1t+1 (rt+1 + qt+1(1− δ))
]
3.5.2 Consumption-good Producing Firms
We specify the production function as:
Yt = AtKαKt HαH
t Heαet
Perfect competition in factor markets implies the following factor prices:
rt = AtF1(Kt, Ht, Het ) = αKAtK
αK−1t HαH
t Heαet =
YtKt
wt = AtF2(Kt, Ht, Het ) = αHAtK
αKt HαH−1
t Heαet =
YtHt
wet = AtF3(Kt, Ht, Het ) = αeAtK
αKt HαH
t Heαe−1t =
YtHet
3.5.3 The Entrepreneur
Entrepreneurs maximise their expected life time utility
E0
[∞∑t=0
(βγ)tcet
](3.5.3.1)
subject to
118
Ket+1 = (ηwet +Ke
t [qt(1− δ) + rt])f(ω(qt))
1− qtg(ω(qt))− cetqt
(3.5.3.2)
Lagrange for the problem:
L = E0
∞∑t=0
βt(cet )+E0
∞∑t=0
βt[λt
((ηwet +Ke
t [qt(1− δ) + rt])f(ω(qt))
1− qtg(ω(qt))− cetqt−Ke
t+1
)]
cet : uce (t)− λt/qt = 0
λt = qt
Ket+1 : −λt + (βγ)Et{λt+1(qt+1(1− δ) + rt+1)
f(ω(qt+1))
(1− qt+1g(ω(qt+1)))} = 0
qt = (βγ)Et[(qt+1(1− δ) + rt+1)
qt+1f(ω(qt+1))
(1− qt+1g(ω(qt+1)))
](3.5.3.3)
3.5.4 Optimal contract
The optimal contract is given by the pair (i, ω) (taking as given net worth n and capital
price q) which solves:
maxi, ω
qif(ω)
subject to
qig(ω) ≥ i− n Lender’s Participation constraint
qif(ω) ≥ n Entrepreneur’s Participation constraint, always satisfied
Technically, only the first constraint binds.
Lagrangian for this problem:
119
L = qif(ω) + λ [qig(ω)− i+ n]
The First Order Conditions:
∂L∂i
= qf(ω) + λ [qg(ω)− 1] = 0 (3.5.4.1)
∂L∂ω
= qif ′(ω) + λqig′(ω) = 0 (3.5.4.2)
∂L∂λ
= qig(ω)− i+ n = 0 (3.5.4.3)
Re-arranging Equation (3.5.4.1):
q
[1
λf(ω) + g(ω)
]= 1
λ = −f′(ω)
g′(ω)
Then, re-arranging Equation (3.5.4.2), we get
1
λ=
g′(ω)
−f ′(ω)=
(1− ζ)(1− Φ(ω))− µφ(ω)
(1− ζ)(1− Φ(ω))= 1− µφ(ω)
(1− ζ)(1− Φ(ω))
Then, combined with Equation (3.3.1.6), we have the following condition:
q
[1− µΦ(ω)− µφ(ω)f(ω)
(1− ζ)(1− Φ(ω))
]= 1 (3.5.4.4)
This can also be written as:
q
[1− µΦ(ω) + µφ(ω)
f(ω)
f ′(ω)
]= 1
3.5.5 Consumption Equivalent Welfare Loss
Let λ denote consumption equivalent welfare loss, the fraction of consumption one
would be willing to give up each period in the economy with perfect enforcement.
120
E(V perfect enforcementt (λ)) = E
[(ln(ct(1 + λ)) + ν(1− Lt)) + βEt
[V perfect enforcementt+1
]]
λ shows up every period and we assume it is deterministic and this reduces to:
E(V perfect enforcementt (λ)) =
1
1− β(1 + λ)+
E[(ln(ct) + ν(1− Lt)) + βEt
[V perfect enforcementt+1
]]
The term in brackets is then:
E(V perfect enforcementt (λ)) =
1
1− β(1 + λ) + E(V perfect enforcement
t )
Then we want to find the λ that equates this with expected welfare in an economy
with limited enforcement. We have:
E(V perfect enforcementt (λ)) = E(V limited enforcement
t )
Or1
1− β(1 + λ) + E(V perfect enforcement
t ) = E(V limited enforcementt )
Then
λ = exp[(1− β)× (E(V limited enforcement
t )− E(V perfect enforcementt ))
]− 1
If we take the economy with perfect enforcement to have higher welfare, then λ <
0. This means you would be willing to give up consumption in the high welfare economy
to have the same welfare as an economy with lower welfare (limited enforcement).
3.5.6 Steady State
The steady state of the model is characterised by:
121
qss =1
[1− µΦss + ωssφssµ fss
f ′ss]
qss =1− (βeγ)rssf ss
[(βeγ)f ss(1− δ) + gss]
Y ss = AssKssαKHssαHHsseαe
Y Kss = Y ss/Kss
rss = αKY Kss
wss = αHYss/Hss
wess = αeYss/Hess
Y Kss =1
αK[1− qssgss
γβf ss− qss(1− δ)]
We calibrate γ such that the steady state internal return is γqssfss
1−qssgss = 1 . Then Y Kss
becomes
Y Kss =1
αK[qss
β− qss(1− δ)]
Kss =
(Y Kss
AssHssαHHessαe
) 1αK−1
Css = ηcess + (1− η)css
Css/Y ss = CY ss
CY ss = 1− δ
Y Kss(1− Φssµ))
iss =δKss
(1− Φssµ)
nss = (1− qssgss) δKss
(1− Φssµ)
kess =nss − ηwess
(qss(1− δ) + rss)=
β
qss(nss − ηwess)
122
ν = wsscss(−1)
cess =qss(f ssiss − kess)
η
css = CY ssY ss
φss = φ(ωss)
Φss = Φ(ωss)
f ss = f(ωss)
gss = g(ωss)
f′ss = f
′(ωss)
123
3.6 Appendix B
3.6.1 Tables
Table 3.6.1.1.: Countries for Empirical Work
CountryAustraliaAustriaBangladeshBelgiumBeninBrazilBurkina FasoCambodiaCentral African RepublicChinaComorosCongo, Dem. Rep.Congo, Rep.DenmarkEthiopiaFinlandFranceGermanyGhanaHungaryIcelandIndonesiaMalawiMaliMozambiqueNigerNigeriaNorwayPapua New GuineaRwandaSierra LeoneSpain
124
Table 3.6.1.2.: Continuation of Countries for Empirical Work
CountrySerbiaPortugalRomaniaSingaporeSlovak RepublicSloveniaSwitzerlandTurkeyUkraineUnited KingdomUnited StatesVietnamZimbabweBhutanBurundiEstoniaGeorgiaIraqKenyaLatviaPhilippinesNetherlandsNew ZealandMacedonia, FYRMoldova
We used data for 57 countries
Table 3.6.1.3.: Summary statistics
Variable Mean Std. Dev. Min. Max. NReal GDP 10.675 1.031 8.57 13.153 513Contract Enforcement 0.552 0.395 -0.518 0.999 510Depth of Credit Info 2.936 2.048 0 6 513
125
3.6.2 Figures
Figure 3.6.2.1.: Scatter: Standard Deviation of GDP and Contract Enforcement
Australia
Austria
Burkina Faso
Cambodia
Denmark
Iceland
MalawiMozambique
Rwanda
Zimbabwe
BhutanBurundi
Estonia
Georgia
Iraq
Kenya Latvia
Macedonia
Moldova
Netherlands
New Zealand
Philippines
Portugal
Romania
Serbia
Singapore
Slovakia
Slovenia
Switzerland
Turkey
Ukraine
UK USA
Vietnam
.05
.1.1
5.2
.25
.3 S
tandard
Devia
tion o
f G
DP
−.5 0 .5 1Contract Enforcement
126
Table
3.6.1.4.:
Fix
edan
dR
andom
Eff
ects
Reg
ress
ion
for
Full
Sam
ple
(57
Cou
ntr
ies)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
RE
FE
RE
FE
RE
FE
FE
RE
Rea
lG
DP
Con
trac
tE
nfo
rcem
ent
0.08
40.
080
0.08
10.
077
0.08
80.
091
[0.0
18]*
**[0
.018
]***
[0.0
18]*
**[0
.018
]***
[0.0
18]*
**[0
.019
]***
Dep
thof
Cre
dit
Info
0.00
80.
008
0.00
80.
008
0.01
70.
017
[0.0
02]*
**[0
.002
]***
[0.0
02]*
**[0
.002
]***
[0.0
04]*
**[0
.004
]***
CO
NE
NF
*DE
PT
HC
RE
DIN
FO
-0.0
15-0
.014
[0.0
06]*
*[0
.006
]**
Con
stan
t10
.560
10.5
6410
.584
10.5
8510
.541
10.5
4710
.547
10.5
41[0
.126
]***
[0.0
11]*
**[0
.112
]***
[0.0
07]*
**[0
.113
]***
[0.0
12]*
**[0
.012
]***
[0.1
14]*
**O
bse
rvat
ions
511
511
513
513
511
511
511
511
Tim
ean
dC
ountr
yF
Ean
dR
E
Sta
nd
ard
erro
rsin
bra
cket
s
*p
¡10%
,**
p¡5
%,
***
p¡1
%
127
Table
3.6.1.5.:
Fix
edan
dR
andom
Eff
ects
Reg
ress
ion
for
Full
Sam
ple
(57
Cou
ntr
ies)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
RE
FE
RE
FE
RE
FE
FE
RE
Rea
lG
DP
Con
trac
tE
nfo
rcem
ent
0.10
50.
096
0.09
00.
081
0.10
50.
113
[0.0
29]*
**[0
.029
]***
[0.0
27]*
**[0
.026
]***
[0.0
27]*
**[0
.027
]***
Dep
thof
Cre
dit
Info
0.03
00.
029
0.02
90.
028
0.04
80.
047
[0.0
03]*
**[0
.003
]***
[0.0
03]*
**[0
.003
]***
[0.0
06]*
**[0
.006
]***
CO
NE
NF
*DE
PT
HC
RE
DIN
FO
-0.0
33-0
.032
[0.0
09]*
**[0
.009
]***
Con
stan
t10
.618
10.6
2610
.589
10.5
9110
.542
10.5
5110
.549
10.5
40[0
.125
]***
[0.0
16]*
**[0
.112
]***
[0.0
09]*
**[0
.112
]***
[0.0
16]*
**[0
.016
]***
[0.1
13]*
**O
bse
rvat
ions
511
511
513
513
511
511
511
511
Cou
ntr
yF
Ean
dR
E
Sta
nd
ard
erro
rsin
bra
cket
s
*p
¡10%
,**
p¡5
%,
***
p¡1
%
128
Table
3.6.1.6.:
Fix
edan
dR
andom
Eff
ects
Reg
ress
ion(3
4C
ountr
ies)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
RE
FE
RE
FE
RE
FE
FE
RE
Rea
lG
DP
Con
trac
tE
nfo
rcem
ent
0.09
20.
091
0.09
10.
089
0.09
60.
097
[0.0
17]*
**[0
.017
]***
[0.0
18]*
**[0
.017
]***
[0.0
18]*
**[0
.019
]***
Dep
thof
Cre
dit
Info
0.00
60.
006
0.00
60.
005
0.01
40.
013
[0.0
03]*
*[0
.002
]**
[0.0
02]*
*[0
.002
]**
[0.0
08]*
[0.0
09]
CO
NE
NF
*DE
PT
HC
RE
DIN
FO
-0.0
13-0
.011
[0.0
12]
[0.0
12]
Con
stan
t10
.529
10.5
3210
.566
10.5
6810
.515
10.5
2010
.517
10.5
13[0
.152
]***
[0.0
12]*
**[0
.121
]***
[0.0
09]*
**[0
.122
]***
[0.0
13]*
**[0
.013
]***
[0.1
23]*
**O
bse
rvat
ions
305
305
306
306
305
305
305
305
Tim
ean
dC
ountr
yF
Ean
dR
E
Sta
nd
ard
erro
rsin
bra
cket
s
*p
¡10%
,**
p¡5
%,
***
p¡1
%
129
Table
3.6.1.7.:
Fix
edan
dR
andom
Eff
ects
Reg
ress
ion
(34
Cou
ntr
ies)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
RE
FE
RE
FE
RE
FE
FE
RE
Rea
lG
DP
Con
trac
tE
nfo
rcem
ent
0.11
60.
112
0.10
40.
099
0.12
60.
129
[0.0
26]*
**[0
.026
]***
[0.0
25]*
**[0
.024
]***
[0.0
25]*
**[0
.026
]***
Dep
thof
Cre
dit
Info
0.02
30.
023
0.02
20.
022
0.05
30.
051
[0.0
03]*
**[0
.003
]***
[0.0
03]*
**[0
.003
]***
[0.0
11]*
**[0
.011
]***
CO
NE
NF
*DE
PT
HC
RE
DIN
FO
-0.0
48-0
.044
[0.0
16]*
**[0
.016
]***
Con
stan
t10
.578
10.5
8210
.572
10.5
7510
.512
10.5
2010
.512
10.5
05[0
.152
]***
[0.0
17]*
**[0
.120
]***
[0.0
10]*
**[0
.121
]***
[0.0
17]*
**[0
.017
]***
[0.1
22]*
**O
bse
rvat
ions
305
305
306
306
305
305
305
305
Cou
ntr
yF
Ean
dR
E
Sta
nd
ard
erro
rsin
bra
cket
s
*p
¡10%
,**
p¡5
%,
***
p¡1
%
130
Chapter 4
Thesis Conclusion
This thesis explores the broad issue of the effects of institutions on macroeconomic per-
formance. The study of the relationship between institutions including the operations
of financial markets, and economic performance has a long history in economics (see
Beck and Levine (2008)). The importance of well-functioning institutions has been
widely documented and is generally accepted (see Knack and Keefer (1995); Rodrik
et al. (2004); Hall and Jones (1999a)). Rodrik et al. (2004) and Hall and Jones (1999a)
observe that good quality institutions is one of the most important factors in raising
per capita output and promoting economic development. Against this background,
we study two areas of institutional imperfection–limited governance of corruption and
limited enforcement of financial contracts. We do so in two main chapters, a brief
summary of each of which is given below.
In the first chapter we study the effects of corruption on sovereign debt decisions.
First, we empirically investigate the determinants of sovereign default. Using various
specifications we find that political stability and corruption increase sovereign default
risk. Second, we setup a dynamic stochastic general equilibrium model to investigate
theoretically the effects of corruption and political risk on sovereign default decisions,
and the implications for macroeconomic activity. Consistent with our empirical results,
we find that corruption can generate high default risk and high credit spreads, but only
when there is enough political stability. In the stable economy with political turnover,
the less corrupt policymakers choose debt levels that would induce a more corrupt
131
policymaker to default. This results in higher credit spreads and higher overall default
rates compared to the case of no turnover or less stability. A seemingly intuitive result
is that a change in power from a less corrupt to a more corrupt government leads to
a greater likelihood of default. This is because of the high level of borrowing by a less
corrupt government, which saddles the more corrupt government with high levels of
debt on which it is induced to default. Our analysis also demonstrates the amplification
effects of corruption on macroeconomic fluctuations, together with the negative effects
of corruption on welfare.
In the second main chapter we study limited contract enforcement in financial
markets and the impact of this on firm financing and aggregate outcomes. As a motiv-
ation, we empirically investigate the effects of limited contract enforcement on output
using panel data. We find that limited enforcement has a negative effect on output and
that this effect is inhibited by poor credit information, although poor credit informa-
tion has negative effect on output. We also find that high costs of contract enforcement
are associated with high output volatility. We then present a dynamic stochastic gen-
eral equilibrium model of asymmetric information and limited contract enforcement
to study the issue theoretically. We show that limited enforcement has effect on a
number of finance variables, such as the leverage of firms, the lending rate and the risk
premium. These effects, all of which are positive, are due to the higher probability
of default when contract enforcement is weaker. An implication is that firms are sub-
ject to tighter credit constraints, the impact of which is most significant for relatively
small firms. Through these channels, we demonstrate how limited enforcement affects
macroeconomic variables, such as output, employment and price. Consistent with our
empirical observations, we find that a higher cost of contract enforcement is associated
with a greater volatility of output.
On the whole, our results indicate that imperfectly-functioning institutions tend
to impede on macroeconomic performance. These results are particularly relevant for
developing countries, where institutions are often weak, fragile and fragmented because
of poor quality of governance. Our analysis suggests that improving such quality has
132
the potential to improve the prospects of such countries.
The current study is limited in many respects. The inability to find suitable
instrumental variables to solve a possible endogeneity problem, in the empirical work
of Chapter (2), is a limitation to the study. In Chapter (2), though the empirical
study could not make use of all possible control variables, the study could still face
limitation for not including for instance external factors as controls. Also, including
more control variables, in the empirical work of the thesis, could enrich our empirical
findings. Though the current study has enriched our understanding of institutions
and macroeconomic performance, possible effects of institutions on key macroeconomic
variables such as monetary policy has not been adequately addressed. The existing
models on institutions (see Huang and Wei (2003, 2006)) find that weak institutions
do not only make monetary policy ineffective but also have serious consequences for
monetary policy targets. We recommend that our model on corruption and sovereign
default be extended to incorporate the monetary policy sector. By this we will be
able to study monetary and fiscal policy interactions in a weak institutional setting
and their consequence on macroeconomic outcomes. Incorporating monetary policy
into the model on limited contract enforcement will improve our understanding of how
effective or ineffective monetary policy will be under limited contract enforcement.
Also introducing habit formation into the utility function will smooth consumption
and enable us understand the behaviour of households towards consumption, in the
present context.
133
BIBLIOGRAPHY
Acemoglu, D. and Johnson, S. (2004). “Institutions as Fundamental Cause of Long-Run
Growth”. NBER Working Papers Series 10481.
Acemoglu, D., Johnson, S., Robinson, J., and Thaicharoen, Y. (2003). “Institutional
causes, macroeconomic symptoms: volatility, crises and growth”. Journal of monet-
ary economics, 50(1):49–123.
Acemoglu, D. and Verdier, T. (1998). “Property Rights, Corruption and Allocation of
Talent: A General Equilibrium Approach”. The Economic Journal 450, 1381–1403.
Acemoglu, D. and Verdier, T. (2000). “The Choice Between Market Failures and
Corruption”. The American Economic Review 1, 194–211.
Aguiar, M. and Gopinath, G. (2006). “Defaultable Debt, Interest Rates and the Current
Account”. Journal of International Economics 69 (June): 64–83.
Al-Marhubi, F. A. (2000). “Corruption and inflation”. Economics Letters, 66(2):199–
202.
Albuquerque, R. and Hopenhayn, H. (2000). “Optimal dynamic lending contracts with
imperfect enforceability”. In AFA 2001 New Orleans Meetings, pages 00–10.
Alfaro, L. and Kanczuk, F. (2005). “Sovereign Debt as a Contingent Claim: A Quant-
itative Approach”. Journal of International Economics 65 (March): 297–314.
Amador, M. (2003). “A Political Economy Model of Sovereign Debt Repayment”.
Stanford University mimeo.
Amaral, P. S. and Quintin, E. (2010). “Limited enforcement, financial intermediation,
and economic development: A quantitative assessment”. International Economic
Review, 51(3):785–811.
134
Arellano, C. (2008). “Default Risk and Income Fluctuations in Emerging Economies”.
American Economic Review 98 (June): 690–712. 19.
Attila, J. (2008). “Corruption, taxation and economic growth: theory and evidence”.
CERDI working paper E 2008.29.
Aylward, M. L. and Thorne, M. R. (1998). “An econometric analysis of countries’ re-
payment performance to the International Monetary Fund”. International Monetary
Fund.
Baldacci, E., Gupta, S., and Mati, A. (2011). “Political and fiscal risk determin-
ants of sovereign spreads in emerging markets”. Review of Development Economics,
15(2):251–263.
Balkan, E. M. (1992). “Political instability, country risk and probability of default”.
Applied Economics, 24(9):999–1008.
Barro, R. (1990). “Government Spending in a Simple Model of Endogenous Growth”.
Journal of Political Economy 98, s103-s117.
Beck, T. and Levine, R. (2008). Legal institutions and financial development. In
Handbook of new institutional economics, pages 251–278. Springer.
Bernanke, B. S., Gertler, M., and Gilchrist, S. (1999). “The financial accelerator in a
quantitative business cycle framework”. Handbook of macroeconomics, 1:1341–1393.
Blackburn and Forgues-Puccio (2010). “Financial Liberalisation, Bureaucratic Corrup-
tion and Economic Development”. Journal of International Money and Finance.
Blackburn, K., Bose, N., and Haque, M. E. (2006). “The incidence and persistence of
corruption in economic development”. Journal of Economic Dynamics and Control,
30(12):2447–2467.
Blackburn, K., Bose, N., and Haque, M. E. (2011). “Public Expenditures, Bureaucratic
Corrruption and Economic Development”. The Manchester School, 79(3):405–428.
135
Blackburn, K. and Forgues-Puccio, G. F. (2007). “Distribution and Development in a
Model of Misgovernance”. European Economic Review, 51(6):1534–1563.
Blackburn, K. and Forgues-Puccio, G. F. (2009). “Why is corruption less harmful in
some countries than in others”? Journal of Economic Behavior & Organization,
72(3):797–810.
Blackburn, K. and Powell, J. (2011a). “Corruption, Inflation and Growth”. Centre
for Growth and Business Cycles Research, Department of Economics, University of
Manchester, UK.
Blackburn, K. and Powell, J. (2011b). “Corruption, inflation and growth”. Economics
Letters, 113(3):225–227.
Blackburn, K. and Sarmah, R. (2008). “Corruption, development and demography”.
Economics of Governance, 9(4):341–362.
Boedo, H. J. M., Senkal, A., and D’Erasmo, P. (2011). “Misallocation, Informality
and Human Capital”. In 2011 Meeting Papers, number 881. Society for Economic
Dynamics.
Bordo, M. and Oosterlinck, K. (2005). “Do political changes trigger debt default? And
do defaults lead to political changes”? In Conference on the Political Economy of
International Finance PEIF.
Braun, M. and Di Tella, R. (2004). “Ination, ination variability, and corruption”.
Economics and Politics, 16(1):77100.
Brown, M., Jappelli, T., and Pagano, M. (2009). “Information sharing and credit:
Firm-level evidence from transition countries”. Journal of Financial Intermediation,
18(2):151–172.
Butler, A. W. and Fauver, L. (2006). “Institutional environment and sovereign credit
ratings”. Financial Management, 35(3):53–79.
136
Carlstrom, C. T. and Fuerst, T. S. (1997). “Agency costs, net worth, and business
fluctuations: A computable general equilibrium analysis”. The American Economic
Review, pages 893–910.
Carlstrom, C. T. and Fuerst, T. S. (1998). “Agency costs and business cycles”. Eco-
nomic Theory, 12(3):583–597.
Carlstrom, C. T. and Fuerst, T. S. (2001). “Monetary shocks, agency costs, and busi-
ness cycles”. In Carnegie-Rochester Conference Series on Public Policy, volume 54,
pages 1–27. Elsevier.
Carlstrom, C. T., Fuerst, T. S., and Paustian, M. (2010). “Optimal monetary policy in
a model with agency costs”. Journal of Money, Credit and Banking, 42(s1):37–70.
Castro, R., Clementi, G. L., and MacDonald, G. (2004). “Investor protection, op-
timal incentives, and economic growth”. The Quarterly Journal of Economics,
119(3):1131–1175.
Castro, R., Clementi, G. L., and MacDonald, G. (2009). “Legal institutions, sec-
toral heterogeneity, and economic development”. The Review of Economic Studies,
76(2):529–561.
Chatterjee, S., Corbae, D., and Rios-Rull, J.-V. (2007). “Credit scoring and competitive
pricing of default risk”. Manuscript, University of Texas at Austin.
Chen, B.-L. (2003). “Tax evasion in a model of endogenous growth”. Review of Eco-
nomic Dynamics, 6(2):381–403.
Ciarlone, A. and Trebeschi, G. (2005). “Designing an early warning system for debt
crises”. Emerging Markets Review, 6(4):376–395.
Ciocchini, F., Durbin, E., and Ng, D. T. (2003). “Does corruption increase emerging
market bond spreads”? Journal of Economics and Business, 55(5):503–528.
Citron, J.-T. and Nickelsburg, G. (1987). “Country risk and political instability”.
Journal of Development Economics, 25(2):385–392.
137
Cole, H. L., Dow, J., and English, W. B. (1995). “Default, Settlement, and Signalling:
Lending Resumption in a Reputational Model of Sovereign Debt”. International
Economic Review 36 (May): 365–85.
Cooley, T., Marimon, R., and Quadrini, V. (2003). “Aggregate consequences of limited
contract enforceability”. Technical report, National Bureau of Economic Research.
Coppier, R. et al. (2006). “Corruption, tax revenue and growth: a non linear relation-
ship”. Rivista di Politica Economica, 96(5/6):243.
Cuadra, G. and Sapriza, H. (2008). “Sovereign Default, Interest Rates and Political
Uncertainty in Emerging Markets”. Journal of International Economics 76 (Septem-
ber): 78–88.
Cule, M. and Fulton, M. (2005). “Some Implications of the Unofficial Economy-
Bureaucratic Corruption Relationship in Transition Countries”. Economics Letters
89, 207–211.
Dal Bo, E. and Rossi, M. A. (2007). “Corruption and inefficiency: Theory and evidence
from electric utilities”. Journal of Public Economics, 91(5):939–962.
De Fiore, F., Teles, P., and Tristani, O. (2011). “Monetary policy and the financing of
firms”. American Economic Journal: Macroeconomics, 3(4):112–142.
D’Erasmo, P. N. and Moscoso Boedo, H. J. (2012). “Financial structure, informality
and development”. Journal of Monetary Economics, 59(3):286–302.
Detragiache, E. and Spilimbergo, A. (2001a). “Crises and liquidity: evidence and
interpretation”. IMF Working Paper.
Detragiache, E. and Spilimbergo, A. (2001b). “Short-term debt and crises”. Interna-
tional Monetary Fund, Washington, DC.
Dixit, A. and Londregan, J. (2000). “Political Power and the Credibility of Government
Debt”. Journal of Economic Theory 94 (September): 80–105.
138
Djankov, S., Glaeser, E., La Porta, R., Lopez-de Silanes, F., and Shleifer, A. (2003).
“The New Comparative Economics.”. NBER Working Papers Series 9608.
Djankov, S., McLiesh, C., and Shleifer, A. (2007). “Private credit in 129 countries”.
Journal of financial Economics, 84(2):299–329.
Djankov, S., Porta, R. L., Lopez-de Silane, F., and Shleifer, A. (2002). “Courts: The
lex mundi project”. Technical report, National Bureau of Economic Research.
Dreher, A. and Herzfeld, T. (2005). “The economic costs of corruption: A survey and
new evidence”. Public Economics, 506001.
Dreher, A. and Siemens, L. (2003). “The intriguing nexus between corruption and
capital account restrictions”. Economics Working Paper Archive at WUSTL.
Eaton, J. and Gersovitz, M. (1981). “Debt with Potential Repudiation: Theoretical
and Empirical Analysis”. Review of Economic Studies 48 (April): 289–09.
Economist., T. (1999). “Argentina’s Next Steps”. The Economist.
Economist, T. (2005). “Argentina’s Debt Restructuring. Tough Deal”. The Economist.
Edwards, S. (1984). “LDC’s foreign borrowing and default risk: an empirical investig-
ation”. National Bureau of Economic Research Cambridge, Mass., USA.
Ehrlich, I. and Lui, F. T. (1999). “Bureaucratic corruption and endogenous economic
growth”. Journal of Political Economy, 107(S6):S270–S293.
Elliott, J. E. (1997). “The role of institutional change in post-Communist transition”.
International Journal of Social Economics, 24(7/8/9):859–872.
Ellis, C. J. and Fender, J. (2006). “Corruption and transparency in a growth model”.
International Tax and Public Finance, 13(2-3):115–149.
Esfahani, H. (2000). “Institutions and Government Controls”. Journal of Development
Economics 63, 197–229.
139
Farida, M. and Ahmadi-Esfahani, F. (2007). “Modelling Corruption in a Cobb-Douglas
Production Function Framework”. Australian Agricultural and Resource Economics
society, 51 st Annual Conference. February 13, 2007.
Feder, G. and Just, R. E. (1977). “A study of debt servicing capacity applying logit
analysis”. Journal of Development Economics, 4(1):25–38.
Frank, C. R. and Cline, W. R. (1971). “Measurement of debt servicing capacity: An
application of discriminant analysis”. Journal of International Economics, 1(3):327–
344.
Ganuza, J.-J. and Hauk, E. (2000). “Economic integration and corruption: The corrupt
soul of the European Union”. Universitat Pompeu Fabra Working Paper.
Gelos, R. G., Sahay, R., and Sandleris, G. (2004). “Sovereign Borrowing by Developing
Countries: What Determines Market Access”? IMFWorking Paper 04/221.
Georgievska, A., Georgievska, L., Stojanovic, A., and Todorovic, N. (2008). “Sovereign
rescheduling probabilities in emerging markets: a comparison with credit rating
agenciesı¿œ ratings”. Journal of Applied Statistics, 35(9):1031–1051.
Gertler, M. (1988). “Financial structure and aggregate economic activity: An over-
view”. Journal of Money, Credit, and Banking, 20(3).
Ghura, M. D. (1998). “Tax Revenue in Sub-Saharan Africa-Effects of Economic Policies
and Corruption”. Number 98-135. International Monetary Fund.
Gomes, J. F., Yaron, A., and Zhang, L. (2003). “Asset prices and business cycles with
costly external finance”. Review of economic Dynamics, 6(4):767–788.
Gupta, S., Davoodi, H., and E, T. (2001). “Corruption and the Provision of Health Care
and Education Services”. In: Jain, A. (Ed.), The Political Economy of Corruption.
Routledge Publishers, London.
Gyimah-Brempong, K. (2002). “Corruption, economic growth, and income inequality
in Africa”. Economics of Governance, 3(3):183–209.
140
Gyimah-Brempong, K., Camacho, D., and Munoz, S. (2006). “Corruption, Growth,
and Income Distribution: Are there Regional Differences”. Economics of Gov-
ernance, 7(3).
Hall, R. E. and Jones, C. I. (1999a). “Why Do Some Countries Produce so much more
Output Per Worker than Others”? The Quarterly Journal of Economics.
Hall, R. E. and Jones, C. I. (1999b). “Why do some countries produce so much more
output per worker than others”? Technical report, National bureau of economic
research.
Haque, N. U. and Sahay, R. (1996). “Do Government Wages Cuts Close Budget
Deficits? The Cost of Corruption”. IMF Staff Papers, Vol. 43, No 4. December, pp.
754-778.
Hatchondo, J. C. and Martinez, L. (2009). “Long-Duration Bonds and Sovereign
Defaults”. Journal of International Economics 79 (September): 117–25.
Hatchondo, J. C. and Martinez, L. (2010.). “The Politics of Sovereign Defaults”.
Economic Quarterly—Volume 96, Number 3—Third Quarter 2010—Pages 291–317.
Hatchondo, J. C., Martinez, L., and Sapriza, H. (2007). “Quantitative models of
sovereign default and the threat of financial exclusion”. Economic Quarterly-Federal
Reserve Bank of Richmond, 93(3):251.
Hatchondo, J. C., Martinez, L., and Sapriza, H. (2007a). “The Economics of Sovereign
Default”. Federal Reserve Bank of Richmond Economic Quarterly 93 (Spring): 163–
87.
Hatchondo, J. C., Martinez, L., and Sapriza, H. (2009). “Heterogeneous Borrowers
in Quantitative Models of Sovereign Default”. International Economic Review 50
(October): 1,129–51.
Hill, I. D. (1973). “Algorithm AS 66: The normal integral”. Journal of the Royal
Statistical Society. Series C (Applied Statistics), 22(3):424–427.
141
Huang, H. and Wei, S.-J. (2003). “Monetary Policies for Developing Countries: The
Role of Corruption”. IMF WORKING PAPER WP/03/183.
Huang, H. and Wei, S.-J. (2006). “Monetary Policies for Developing Countries: The
Role of Institutional Quality”. Journal of International Economics.
Imam, P. A. and Jacobs, D. (2014). “Effect of Corruption on Tax Revenues in the
Middle East”. Review of Middle East Economics and Finance Rev. Middle East
Econ. Fin., 10(1):1–24.
IMF. “The IMF and Argentina, 1991–2001”. Independent Evaluation Office Re-
port.Washington, D.C.: IMF.
IMF (2002a). “Sovereign Debt Restructurings and the Domestic Economy Experience
in Four Recent Cases”. Washington, D.C.: IMF (February 21).
IMF (2003). “Lessons from the Crisis in Argentina”. Washington, D.C.: IMF (March
24). IMF. 2004.
Infante, D. and Smirnova, J. (2009). “Market Failures Within Poor Institutions: The
Effects of Bureaucrats Rent-Seeking Activity”. In: Salvadori, N. (Ed.), Institutional
and Social Dynamics of Growth and Distribution. Edward Elgar, pp. 94–116.
Jappelli, T. and Pagano, M. (2002). “Information sharing, lending and defaults: Cross-
country evidence”. Journal of Banking & Finance, 26(10):2017–2045.
Johnson, S., Kaufmann, D., and Shleifer, A. (1997). “The unofficial economy in trans-
ition”. Brookings Papers on Economic Activity 2: 159-221.
Johnson, S., Kaufmann, D., and Zoido-Lobaton, P. (1998). “Corruption, Public Fin-
ances and the Unofficial Economy”. World Bank Policy Research Working Paper
Series 2169.
Johnson, S., Kaufmann, D., and Zoido-Lobaton, P. (1999). “Corruption, public finances
and the unofficial economy”., volume 2169. World Bank Publications.
142
Kalliomaki, M. (2012). “Determinants of Sovereign Defaults”.
https://lup.lub.lu.se/student-papers/search/publication/2338226.
Kauppi, H. and Saikkonen, P. (2008). “Predicting US recessions with dynamic binary
response models”. The Review of Economics and Statistics, 90(4):777–791.
Keith, B., Neanidis Kyriakos, C., and Emranul, H. M. (2008). “Corruption, seigniorage
and growth: theory and evidence”. Technical report, CESinfo Working Paper Series.
Munich: CESifo Group.
Khan, A. and Ravikumar, B. (2001). “Growth and risk-sharing with private informa-
tion”. Journal of Monetary Economics, 47(3):499–521.
Klein, P., Krusell, P., and Rios-Rull, J.-V. (2008). “Time-consistent public policy”.
The Review of Economic Studies, 75(3):789–808.
Knack, S. and Keefer, P. (1995). “Institutions and Economic Performance: Cross-
Country Tests Using Alternative Institutional Measures”. Economics and Politics,
vol. 7, no. 3, pp. 207-227.
Kraay, A. and Nehru, V. (2006). “When is external debt sustainable”? The World
Bank Economic Review, 20(3):341–365.
Krusell, P. and Smith Jr, A. A. (2003). “Consumption–savings decisions with quasi–
geometric discounting”. Econometrica, 71(1):365–375.
La Porta, R., Lopez-de Silanes, F., Shleifer, A., and Vishny, R. (2000). “Investor
protection and corporate governance”. Journal of financial economics, 58(1):3–27.
La Porta, R., Lopez-de Silanes, F., Shleifer, A., and Vishny, R. W. (1997). “Legal
determinants of external finance”. National bureau of economic research.
Lausev, J., Stojanovic, A., and Todorovic, N. (2011). “Determinants of debt reschedul-
ing in Eastern European countries”. Economic Annals, 56(188):7–31.
143
Levin, A. T., Natalucci, F. M., and Zakrajsek, E. (2004). “The magnitude and cyclical
behavior of financial market frictions”.
Levine, R., Loayza, N., and Beck, T. (2000). “Financial intermediation and growth:
Causality and causes”. Journal of monetary Economics, 46(1):31–77.
Li, C. A. (1992). “Debt arrears in Latin America: Do political variables matter”? The
Journal of Development Studies, 28(4):668–688.
Li, H., Xu, L. C., and Zou, H.-f. (2000). “Corruption, income distribution, and growth”.
Economics & Politics, 12(2):155–182.
Lopez de Silanes, F., La Porta, R., Shleifer, A., and Vishny, R. (1998). “Law and
finance”. Journal of political economy, 106:1113–1155.
Lucas, R. E. (1987). “Models of business cycles”, volume 26. Basil Blackwell Oxford.
Marcet, A. and Marimon, R. (1992). “Communication, commitment, and growth”.
Journal of Economic Theory, 58(2):219–249.
Mauro, P. (1995). “Corruption and Growth”. The Quarterly Journal of Economics 3,
681–712.North, D.C., 1997. The contribution of the new institutional economics to
an understanding of the transition problem. WIDER Annual Lectures, p. 1.
Mauro, P. (1996). “The Effects of Corruption on Growth, Investment, and Government
Expenditure”. IMF WORKING PAPER.
Mauro, P. (1997a). “The Effects of Corruption on Growth, Investment, and Gov-
ernment Expenditure: A Cross–Country Analysis. Corruption and the Global Eco-
nomy”. Washington D.C, Institute for International Economics: 83–107.
Mauro, P. (1997b). “Why Worry About Corruption”. Washington D.C., International
Monetary Fund.
Mauro, P. (1998). “The effects of corruption on growth, investment, and government
expenditure: a cross-country analysis”. In: Elliott, K.A. (Ed.), Corruption and the
Global Economy. Institute for International Economics, Washington D.C.
144
McFadden, D., Eckaus, R., Feder, G., Hajivassiliou, V., and O’Connell, S. (1985). “Is
there life after debt? An econometric analysis of the creditworthiness of developing
countries”. International debt and the developing countries, pages 179–209.
Min, H. G. (1998). “Determinants of emerging market bond spread: do economic
fundamentals matter”? Number 1899. World Bank Publications.
Monge-Naranjo, A. (2009). “Entrepreneurship and firm heterogeneity with limited
enforcement”. Annals of Finance, 5(3-4):465–494.
Moser, C. (2007). “The impact of political risk on sovereign bond spreads-evidence
from Latin America”. In Proceedings of the German Development Economics Con-
ference, Gottingen 2007, number 24. Verein fur Socialpolitik, Research Committee
Development Economics.
Murphy, K., Shleifer, A., and Vishny, R. (1991). “The Allocation of Talent: Implica-
tions for Growth”. The Quarterly Journal of Economics.
Ng, E. C. (2012). “Forecasting US recessions with various risk factors and dynamic
probit models”. Journal of Macroeconomics, 34(1):112–125.
North, D. C. (1989). “Institutions and economic growth: An historical introduction”.
World development, 17(9):1319–1332.
North, D. C. (1990). “Institutions, institutional change and economic performance”.
Cambridge university press.
Nyberg, H. (2010). “Dynamic probit models and financial variables in recession fore-
casting”. Journal of Forecasting, 29(1-2):215–230.
Ofer, G. (2003). “Transition and Development Economies: Comparing the Quality of
Governments”. In:Campos, N., Fidrmuc, J. (Eds.), Political Economy of Transition
and Development. Kluwer Academic Publishers, pp. 69–96.
Ortigueira, S., Pereira, J., and Pichler, P. (2012). “Markov-perfect optimal fiscal policy:
the case of unbalanced budgets”.
145
Perri, F. and Neumeyer, A. (2004). “Emerging Market Business Cycles: The Role of
Interest Rates”. NBER working paper, 10387.
Pestova, A. (2015). “Leading Indicators of the Business Cycle: Dynamic Logit Models
for OECD Countries and Russia”. Higher School of Economics Research Paper No.
WP BRP, 94.
PRS (2008). “A Business Guide to Political Risk for International De-
cisions”.International Country Risk Guide (ICRG).Part II. 2008.
Quintin, E. (2000). “Limited enforcement and the organization of production”. Un-
published manuscript, Federal Reserve Bank of Dallas.
Rahnama-Moghadam, M. (1995). “Debt rescheduling in less-developed countries: world
or regional crisis”. The Journal of Developing Areas, pages 11–22.
Reinhart, C. M., Rogoff, K. S., and Savastano, M. A. (2003). “Debt intolerance”.
Technical report, National Bureau of Economic Research.
Rodrik, D., Subramanian, A., and Trebbi, F. (2004). “Institutions rule: the primacy
of institutions over geography and integration in economic development”. Journal
of economic growth, 9(2):131–165.
Rose, A. K. (2005). “One reason countries pay their debts: renegotiation and interna-
tional trade”. Journal of development economics, 77(1):189–206.
Rowland, P. and Torres, J. (2004). “Determinants of spread and creditworthiness for
emerging market sovereign debt: a panel data study”. Im Internet: http://www.
banrep. gov. co/docum/ftp/borra295. pdf (abgerufen am 22.03. 08).
Santiso, J. (2003). “The political economy of emerging markets: Actors, institutions
and financial crises in Latin America”. Palgrave Macmillan.
Sarte, P.-D. G. (2000). “Informality and rent-seeking bureaucracies in a model of
long-run growth”. Journal of Monetary Economics, 46(1):173–197.
146
Schimmelpfennig, M. A., Roubini, N., and Manasse, P. (2003). “Predicting sovereign
debt crises”. Number 3-221. International Monetary Fund.
Steinberg, J. B. (2013). “Information, Contract Enforcement, and Misallocation”. Job
Market Paper.
Sturzenegger, F. and Zettelmeyer, J. (2006). “Debt defaults and lessons from a decade
of crises”. MIT press.
Swaleheen, M. (2011). “Economic growth with endogenous corruption: an empirical
study”. Public Choice, 146(1-2):23–41.
Tanzi, V. (1998). “Corruption Around the World: Causes, Consequences, Scope, and
Cures”. Working Paper No. 63 (Washington, DC: International Monetary Fund).
Tanzi, V. and Davoodi, H. (1997). “Corruption, Public Investment and Growth”. IMF
Working paper.
Tanzi, V. and Davoodi, H. (2000). “Corruption, growth, and public finances”. IMF
Working Paper.
Tauchen, G. (1986). “Finite state markov-chain approximations to univariate and
vector autoregressions”. Economics letters, 20(2):177–181.
Tomz, M. and Wright, M. L. J. (2007). “Do Countries Default in Bad Times”? Journal
of the European Economic Association 5: 352-60.
Treisman, D. (2003). “Postcommunist corruption”. Political Economy of Transition
and Development: Institutions, Policies and Politics, pages 201–26.
Ul Haque, N., Mark, N. C., and Mathieson, D. J. (1998). “The relative importance of
political and economic variables in creditworthiness ratings”. IMF working paper.
Van Rijckeghem, C. and Weder, B. (2004). “The politics of debt crises”. CEPR
Discussion Paper.
147
Verma, S. (2002). “Determinants of Sovereign Defaults: What Does the Empirical
Evidence Tell Us”? Economic and Political Weekly, pages 4817–4822.
Wei, S.-J. (1997). “Why is Corruption so much more Taxing than Tax?. Arbitrariness
Kills”. NBER Working Paper 6255, November.
Williams, A. and Siddique, A. (2008). “The use (and abuse) of governance indicators
in economics: a review”. Economics of Governance, 9(2):131–175.
Williams, B. (2014). “Bank risk and national governance in Asia”. Journal of Banking
& Finance, 49:10–26.
Yue, V. Z. (2006). “Sovereign Default and Debt Renegotiation”. Manuscript, New
York University.
148
Appendix A
Computer Codes
A.1 Chapter 2 Computer Codes
A.1.1 STATA CODES
This Stata code is used for the empirical results of this chapter of the thesis.
Listing A.1: Stata Do File
// import data// use sove r e i gn . dta ” , c l e a regen id = group ( country )x t s e t id year
// i c r g c= measure o f co r rupt i on// prr = measure p o l i t i c a l s t a b i l i t y// lgdppc= log GDP per cap i ta//gdpgww= GDP growth// extdebtperc= e x t e r n a l debt−GDP r a t i o// de f= d e f a u l t
// i c r g c 1= one per iod lag o f co r rupt i on// prr1 = one per iod lag o f p o l i t i c a l s t a b i l i t y// lgdppc1= one per iod lag o f l og GDP per cap i ta//gdpgww1= one per iod lag o f GDP growth// extdebtperc1= one per iod lag o f e x t e r n a l debt−GDP r a t i o// de f1= one per iod lag o f d e f a u l t
//CORRELATIONSc o r r t e x de f i c r g c prr lgdppc gdpgww extdebtperc ,
//SUMMARY STATISTICSsutex de f i c r g c prr lgdppc gdpgww extdebtperc , minmax
149
////CURRENT EXPLANATORY VARIABLES ONLYprob de f i c r g c prr extdebtperc gdpgwwe s t s t o PROB1
prob de f i c r g c prr extdebtperc lgdppce s t s t o PROB2
prob de f i c r g c prr extdebtperc gdpgww lgdppce s t s t o PROB3
//mfxprob de f i c r g c prr extdebtperc gdpgwwmfxe s t s t o mfx1
prob de f i c r g c prr extdebtperc lgdppcmfxe s t s t o mfx2
prob de f i c r g c prr extdebtperc gdpgww lgdppcmfxe s t s t o mfx3
//WITH LAGGED DEFAULT
prob de f de f1 i c r g c 1 prr1 extdebtperc1 gdpgww1e s t s t o PROB1
prob de f de f1 i c r g c 1 prr1 extdebtperc1 lgdppc1e s t s t o PROB2
prob de f de f1 i c r g c 1 prr1 extdebtperc1 gdpgww1 lgdppc1e s t s t o PROB3
prob de f de f1 i c r g c 1 prr1 extdebtperc1 gdpgww1mfxe s t s t o mfx1
prob de f de f1 i c r g c 1 prr1 extdebtperc1 lgdppc1mfxe s t s t o mfx2
prob de f de f1 i c r g c 1 prr1 extdebtperc1 gdpgww1 lgdppc1mfxe s t s t o mfx3
150
//ONLY LAGGED EXPLANATORY VARIABLES; NO LAGGED DEFAULT
prob de f i c r g c 1 prr1 extdebtperc1 gdpgww1e s t s t o PROB1
prob de f i c r g c 1 prr1 extdebtperc1 lgdppc1e s t s t o PROB2
prob de f i c r g c 1 prr1 extdebtperc1 gdpgww1 lgdppc1e s t s t o PROB3
//MFX
prob de f i c r g c 1 prr1 extdebtperc1 gdpgww1mfxe s t s t o mfx1
prob de f i c r g c 1 prr1 extdebtperc1 lgdppc1mfxe s t s t o mfx2
prob de f i c r g c 1 prr1 extdebtperc1 gdpgww1 lgdppc1mfxe s t s t o mfx3
151
A.1.2 FORTRAN CODES
We use fortran to solve the theoretical model by value function iteration. corruption-
model.f90 is the main program which drives the value function iteration (vfi module.f90)
and the simulation (sim module.f90). The code makes use of the fortran library (func-
tion) alnorm by Hill (1973) to compute the cumulative density function of the standard
normal distribution (https://people.sc.fsu.edu/˜jburkardt/f77 src/asa066/asa066.html
for code). To run these programs we also need other modules which include:
i. grid construction.f90 which constructs the grids for the programs.
ii. model tools.f90 which creates and save the parameters for solving the programs.
iii. data output.f90, a module for saving data from the programs.
iv. array tools.f90 for sorting arrays and array structures.
v. input param.txt; this contains the parameter values to be used by the variousprograms.
Listing A.2: Value Function Iteration
module v f i module
use mode l too l s
use omp lib
i m p l i c i t none
type s o l u t i o n v a r s
r e a l (8 ) : : va l ! opt imal va lue
r e a l (8 ) : : bn so l ! b ’ cho i c e
i n t e g e r : : b n s o l i d x ! index f o r b ’
r e a l (8 ) : : c s o l ! consumption cho i c e
end type s o l u t i o n v a r s
conta in s
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine v a l f c n i t e r
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
152
subrout ine v a l f c n i t e r ( n b , n y , b gr id , y gr id , Py , &
Py cdf ,pm, q , p d , ystar , d po l i cy , c p o l i c y , &
bn po l i cy , b n i d x p o l i c y )
i m p l i c i t none
in t ege r , i n t e n t ( in ) : : n b , n y
r e a l ( 8 ) , dimension ( n b ) , i n t e n t ( in ) : : b g r i d
r e a l ( 8 ) , dimension ( n y ) , i n t e n t ( in ) : : y g r i d
r e a l ( 8 ) , dimension ( n y , n y ) , i n t e n t ( in ) : : Py
r e a l ( 8 ) , dimension ( n y , n y ) , i n t e n t ( in ) : : Py cdf
type ( params ) , i n t e n t ( in ) : : pm
! p o l i c y f u n c t i o n s ( output )
r e a l ( 8 ) , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( out ) : : q
! q (b ’ , y , d , type ) , q schedu le
r e a l ( 8 ) , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( out ) : : p d
! p d (b ’ , y , h ’ , type ’ ) , d e f a u l t p r o b a b i l i t y
in t ege r , dimension ( n b , 2 , 2 ) , i n t e n t ( out ) : : y s ta r
! y∗(b ’ , h ’ , type ’ ) , d e f a u l t t h r e s h o l d s
l o g i c a l , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( out ) : : d p o l i c y
! d (b , y , h i s t , type ) , d e f a u l t p o l i c y
r e a l ( 8 ) , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( out ) : : c p o l i c y
! d (b , y , h i s t , type ) , d e f a u l t p o l i c y
r e a l ( 8 ) , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( out ) : : bn po l i cy
! b ’ ( b , y , h i s t , type ) , debt p o l i c y
in t ege r , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( out ) : : b n i d x p o l i c y
! b ’ ( b , y , h i s t , type ) , debt p o l i c y ( index )
! %%%%%%%%%%%%%%%%%
! l o c a l a r rays
! %%%%%%%%%%%%%%%%%
! make a l l o c a t a b l e , to avoid memory problems
r e a l ( 8 ) , a l l o c a t a b l e , dimension ( : , : , : , : ) : : v , v0
! v (b , y , h , type )
r e a l ( 8 ) , a l l o c a t a b l e , dimension ( : , : , : , : ) : : vhat , vhat0
! vhat (b , y , h , type )
r e a l ( 8 ) , a l l o c a t a b l e , dimension ( : , : , : ) : : vd , vd0
! v d (y , h , type ) , va lue o f d e f a u l t
r e a l ( 8 ) , a l l o c a t a b l e , dimension ( : , : , : , : ) : : vnd , vnd0
153
! v nd (b , y , h , type ) , va lue o f not d e f a u l t i n g
r e a l ( 8 ) , a l l o c a t a b l e , dimension ( : , : , : , : ) : : cv
! cv (b ’ , y , d , type ) , cont inuat i on va lue s
! l o c a l v a r i a b l e s
in t ege r , parameter : : MAX ITER = 1000
r e a l ( 8 ) , parameter : : TOL = 1.0 d−6
r e a l (8 ) : : e r r v , e r r vha t
i n t e g e r : : i t e r , e f l a g
i n t e g e r : : i b , i y , i type , i h
l o g i c a l : : de f
type ( s o l u t i o n v a r s ) : : so l nd , s o l d
! A l l o ca t e l o c a l a r rays
a l l o c a t e ( v ( n b , n y , 2 , 2 ) , v0 ( n b , n y , 2 , 2 ) , &
vhat ( n b , n y , 2 , 2 ) , vhat0 ( n b , n y , 2 , 2 ) )
a l l o c a t e ( vnd ( n b , n y , 2 , 2 ) , vnd0 ( n b , n y , 2 , 2 ) )
a l l o c a t e ( vd ( n y , 2 , 2 ) , vd0 ( n y , 2 , 2 ) )
a l l o c a t e ( cv ( n b , n y , 2 , 2 ) )
! i n i t i a l i z e i t e r a t i o n
e f l a g = 0
i t e r = 0
! i n i t i a l i z e va lue f u n c t i o n s
c a l l i n i t v f i ( n b , n y , pm, v0 , vnd0 , vd0 , vhat0 )
do whi l e ( e f l a g == 0)
! compute bond p r i c e schedule , d e f a u l t c u t o f f s and prob o f
! d e f a u l t
c a l l c a l c b o n d p r i c e s c h e d u l e ( n b , n y , vnd0 , vd0 ,&
Py cdf ,pm, q , p d , y s ta r )
! compute cont inuat i on values , CV(b ’ , y , d , j )
! b ’ == debt choice , y = cur rent y , d = d e f a u l t cho i c e today ,
! j = type today
c a l l c a l c c v ( n b , n y , v0 , vhat0 , Py , pm, cv )
154
! then compute optimal cho i ce s , update vd , vnd , v and p o l i c y
! r u l e s
! loop over y f i r s t to take advantage o f OpenMP
! $omp p a r a l l e l do p r i va t e ( i type , i h , i y , i b , def ,&
so l d , s o l nd )
do i y = 1 , n y ! endowment y
do i t y p e = 1 ,2 ! gov type , c u r r e n t l y in power
do i h = 1 ,2 ! cur r ent h i s t o r y h
! compute value o f d e f a u l t i n g
de f = . t rue .
i b = 1
! s e t i b = 1 ( sove r e i gn i s d e f a u l t i n g anyway )
c a l l s o l v e g r i d s e a r c h ( n b , n y , i b , i y , i h ,&
i type , def , b gr id , y gr id , q , cv , pm, s o l d )
vd ( i y , i h , i t y p e ) = s o l d%va l
do i b = 1 , n b ! debt / a s s e t s b
! compute value o f not d e f a u l t i n g
de f = . f a l s e .
c a l l s o l v e g r i d s e a r c h ( n b , n y , i b , i y ,&
i h , i type , def , b gr id , y gr id , q , cv ,&
pm, so l nd )
vnd ( i b , i y , i h , i t y p e ) = so l nd%val
i f ( s o l nd%val >= s o l d%val ) then
d p o l i c y ( i b , i y , i h , i t y p e ) =&
. f a l s e .
c p o l i c y ( i b , i y , i h , i t y p e ) =&
so l nd%c s o l
bn po l i cy ( i b , i y , i h , i t y p e)=&
so l nd%bn so l
b n i d x p o l i c y ( i b , i y , i h , i t y p e )&
= so l nd%b n s o l i d x
v ( i b , i y , i h , i t y p e ) = &
so l nd%val
155
e l s e
d p o l i c y ( i b , i y , i h , i t y p e )= &
. true .
c p o l i c y ( i b , i y , i h , i t y p e )= &
s o l d%c s o l
bn po l i cy ( i b , i y , i h , i t y p e)=&
s o l d%bn so l
b n i d x p o l i c y ( i b , i y , i h ,&
i t y p e ) = s o l d%b n s o l i d x
v ( i b , i y , i h , i t y p e ) =&
s o l d%va l
end i f
end do
end do
end do
end do
! $omp end p a r a l l e l do
! now update value when not in government
c a l l update vhat ( n b , n y , Py , v0 , vhat0 , d po l i cy ,&
c p o l i c y , bn idx po l i cy , pm, vhat )
! compute convergence e r r o r
e r r v = maxval ( abs ( v − v0 ) / abs ( v0 ) ) ;
e r r vha t = maxval ( abs ( vhat − vhat0 ) / abs ( vhat0 ) ) ;
i f (mod( i t e r , 10) == 0) then
p r i n t ∗ , ” i t e r = ” , i t e r , ” e r r = ” , max( er r v , &
e r r vha t )
end i f
! a l l r e tu rn s t rue i f a l l e lements in the array are t rue
i f ( a l l ( abs (v−v0 ) <= TOL∗abs ( v0 ) ) . and . a l l (&
abs ( vhat−vhat0 ) <= TOL∗abs ( vhat0 ) ) ) then
e f l a g = 1 ;
end i f
i t e r = i t e r + 1 ;
156
i f ( i t e r >= MAX ITER) then
p r i n t ∗ , ”Maximum I t e r a t i o n s Reached”
e f l a g = 2 ;
end i f
! update guess
v0 = v ;
vnd0 = vnd
vd0 = vd
vhat0 = vhat
end do
! save r e s u l t s
c a l l s a v e v f i r e s u l t s ( n b , n y , b gr id , y gr id , v , vnd,&
vd , vhat , d po l i cy , c p o l i c y , q , bn po l i cy )
end subrout ine v a l f c n i t e r
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine i n i t v f i
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗subrout ine i n i t v f i ( n b , n y , pm, v0 , vnd0 , vd0 , vhat0 )
i m p l i c i t none
in t ege r , i n t e n t ( in ) : : n b , n y
type ( params ) , i n t e n t ( in ) : : pm
r e a l ( 8 ) , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( out ) : : v0
r e a l ( 8 ) , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( out ) : : vnd0
r e a l ( 8 ) , dimension ( n y , 2 , 2 ) , i n t e n t ( out ) : : vd0
r e a l ( 8 ) , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( out ) : : vhat0
l o g i c a l : : l o a d i n i t i a l g u e s s
i n t e g e r : : i n f i l e = 109
l o a d i n i t i a l g u e s s = ( . not . pm%new v0 )
i f ( l o a d i n i t i a l g u e s s ) then
157
open ( i n f i l e , f i l e = ” r e s u l t s / guess v0 . txt ”)
read ( i n f i l e , ∗ ) v0
rewind ( i n f i l e )
c l o s e ( i n f i l e )
open ( i n f i l e , f i l e = ” r e s u l t s / guess vnd0 . txt ”)
read ( i n f i l e , ∗ ) vnd0
rewind ( i n f i l e )
c l o s e ( i n f i l e )
open ( i n f i l e , f i l e = ” r e s u l t s / guess vd0 . txt ”)
read ( i n f i l e , ∗ ) vd0
rewind ( i n f i l e )
c l o s e ( i n f i l e )
open ( i n f i l e , f i l e = ” r e s u l t s / guess vhat0 . txt ”)
read ( i n f i l e , ∗ ) vhat0
rewind ( i n f i l e )
c l o s e ( i n f i l e )
e l s e
vd0 = 0 .0
vnd0 = 0 .0
v0 = 0 .0 ! equal to max( vd0 , vnd0 )
vhat0 = 0 .0
end i f
end subrout ine i n i t v f i
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine update vhat
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗subrout ine update vhat ( n b , n y , Py , v0 , vhat0 , d po l i cy ,&
c p o l i c y , bn idx po l i cy , pm, vhat )
i m p l i c i t none
in t ege r , i n t e n t ( in ) : : n b , n y
r e a l ( 8 ) , dimension ( n y , n y ) , i n t e n t ( in ) : : Py
r e a l ( 8 ) , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( in ) : : v0
r e a l ( 8 ) , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( in ) : : vhat0
158
l o g i c a l , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( in ) : : d p o l i c y
r e a l ( 8 ) , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( in ) : : c p o l i c y
in t ege r , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( in ) : : &
b n i d x p o l i c y
type ( params ) , i n t e n t ( in ) : : pm
r e a l ( 8 ) , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( out ) : : vhat
! l o c a l a r rays
r e a l ( 8 ) , dimension ( n y ) : : vnext
! l o c a l v a r i a b l e s
i n t e g e r : : i t , i h , i y , i b
i n t e g e r : : i t o t h e r , i d o t h e r , bn idx othe r
r e a l (8 ) : : c o ther , u , cv hat va l , p i t u r n o t h e r
l o g i c a l : : d e f o t h e r
! now , g iven updated p o l i c y funct i ons , update value o f
! government not in power
do i t = 1 ,2 ! government type
i f ( i t == 1) then
i t o t h e r = 2 ! HIGH type i s in power
p i t u r n o t h e r = pm%piH /0 .4
e l s e
i t o t h e r = 1 ! LOW type i s in power
p i t u r n o t h e r = pm%piL /0 .9
end i f
do i h = 1 ,2 ! cur r ent h i s t o r y h
do i y = 1 , n y ! endowment y
do i b = 1 , n b ! debt / a s s e t s b
! get consumption o f other government
c o t he r = c p o l i c y ( i b , i y , i h , i t o t h e r )
! c a l c u l a t e u t i l i t y f l ows to gov ’ t out o f power
u = c a l c u t i l i t y ( c other , pm)
! get d e f a u l t p o l i c y o f other government
d e f o t h e r = d p o l i c y ( i b , i y , i h , i t o t h e r )
159
i f ( d e f o t h e r ) then
i d o t h e r = 2
e l s e
i d o t h e r = 1
end i f
! get b ’ p o l i c y ( index ) o f other government
bn idx othe r = b n i d x p o l i c y ( i b , i y , i h , i t o t h e r )
! compute cont inuat i on value
! with prob p i tu rn o the r , t h i s type t r a n s i t i o n s
! i n to power and r e c e i v e s v0
! with prob 1−p i tu rn o the r , t h i s type s tays out
! o f pwer and r e c e i v e s vhat0
vnext = p i t u r n o t h e r ∗ v0 ( bn idx other , : , i d o t h e r , i t )&
+ (1− p i t u r n o t h e r )∗ vhat0 ( bn idx other , : , i d o t h e r , i t )
c v h a t v a l = DOT PRODUCT( Py( i y , : ) , vnext )
vhat ( i b , i y , i h , i t ) = u + pm%beta ∗ c v h a t v a l
end do
end do
end do
end do
end subrout ine update vhat
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine c a l c u t i l i t y
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗f unc t i on c a l c u t i l i t y ( c , pm) r e s u l t (u)
i m p l i c i t none
r e a l ( 8 ) , i n t e n t ( in ) : : c
type ( params ) , i n t e n t ( in ) : : pm
r e a l (8 ) : : u ! output
i f (pm%sigma == 1) then
u = log ( c )
e l s e
160
u = c∗∗(1−pm%sigma ) / (1−pm%sigma )
end i f
end func t i on c a l c u t i l i t y
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine ca lc consumpt ion
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗f unc t i on ca lc consumpt ion ( n b , n y , i b , i y , i h , i t ,&
i bn , def , b gr id , y gr id , q , pm) r e s u l t ( c )
i m p l i c i t none
in t ege r , i n t e n t ( in ) : : n b , n y , i b , i y , i h , i t , i bn
l o g i c a l : : de f
r e a l ( 8 ) , dimension ( n b ) , i n t e n t ( in ) : : b g r i d
r e a l ( 8 ) , dimension ( n y ) , i n t e n t ( in ) : : y g r i d
r e a l ( 8 ) , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( in ) : : q
type ( params ) , i n t e n t ( in ) : : pm
r e a l (8 ) : : c , bn val , b val , tau , h val , q va l
i n t e g e r : : i d
! d e f a u l t d e c i s i o n
i f ( de f ) then
i d = 2
e l s e
i d = 1
end i f
! get b ’ cho i c e
bn val = b gr id ( i bn )
! tax ra t e depends on cur rent government type
i f ( i t == 1) then
tau = pm%tauL
e l s e
tau = pm%tauH
end i f
161
! cu r r ent h i s t o r y
i f ( i h == 1) then
h va l = 0 .0
e l s e
h va l = 1 .0
end i f
! bond p r i c e
q va l = q ( i bn , i y , i d , i t ) ! i d = 1 ( no d e f a u l t ) ,
! i d == 2 ( d e f a u l t )
! compute consumption
c = (1−tau ) ∗ (1−h va l ∗pm%lambda )∗ exp ( y g r i d ( i y ) ) −&
q va l ∗bn val
i f ( . not . de f ) then
b va l = b gr id ( i b )
c = c + b va l
end i f
end func t i on ca lc consumpt ion
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine c a l c v a l
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗f unc t i on c a l c v a l ( n b , n y , i b , i y , i h , i t , i bn , def , &
b gr id , y gr id , q , cv , pm) r e s u l t ( va l )
i m p l i c i t none
in t ege r , i n t e n t ( in ) : : n b , n y , i b , i y , i h , i t , i bn
l o g i c a l : : de f
r e a l ( 8 ) , dimension ( n b ) , i n t e n t ( in ) : : b g r i d
r e a l ( 8 ) , dimension ( n y ) , i n t e n t ( in ) : : y g r i d
r e a l ( 8 ) , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( in ) : : q
r e a l ( 8 ) , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( in ) : : cv
type ( params ) , i n t e n t ( in ) : : pm
r e a l (8 ) : : va l ! output
r e a l (8 ) : : q va l , c , u , d val , tau , h val , bn val , b val , &
cv va l
162
i n t e g e r : : i d
! d e f a u l t d e c i s i o n
i f ( de f ) then
i d = 2
e l s e
i d = 1
end i f
! compute consumption
c = calc consumpt ion ( n b , n y , i b , i y , i h , i t , i bn ,&
def , b gr id , y gr id , q , pm)
i f ( c > 0 . 0 ) then
! c a l c u l a t e u t i l i t y from consumption
u = c a l c u t i l i t y ( c , pm)
! get cont inuat i on value
cv va l = cv ( i bn , i y , i d , i t )
! compute value o f not d e f a u l t
va l = u + pm%beta ∗ cv va l
e l s e
va l = −huge ( va l )
end i f
end func t i on c a l c v a l
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine s o l v e g r i d s e a r c h
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗subrout ine s o l v e g r i d s e a r c h ( n b , n y , i b , i y , i h , i t ,&
def , b gr id , y gr id , q , cv , pm, s o l )
i m p l i c i t none
in t ege r , i n t e n t ( in ) : : n b , n y , i b , i y , i h , i t
l o g i c a l , i n t e n t ( in ) : : de f
r e a l ( 8 ) , dimension ( n b ) , i n t e n t ( in ) : : b g r i d
r e a l ( 8 ) , dimension ( n y ) , i n t e n t ( in ) : : y g r i d
163
r e a l ( 8 ) , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( in ) : : q
r e a l ( 8 ) , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( in ) : : cv
type ( params ) , i n t e n t ( in ) : : pm
type ( s o l u t i o n v a r s ) , i n t e n t ( out ) : : s o l
! l o c a l a r rays
r e a l ( 8 ) , dimension ( n b ) : : v a l g r i d
! l o c a l v a r i a b l e s
i n t e g e r : : i bn , b n s o l i d x
i n t e g e r : : dbg f l a g = 0
i n t e g e r : : ou t un i t = 96
! compute val nd , va l d f o r each b ’ on g r id
do i bn = 1 , n b
v a l g r i d ( i bn ) = c a l c v a l ( n b , n y , i b , i y , i h , i t , &
i bn , def , b gr id , y gr id , q , cv , pm)
end do
i f ( dbg f l ag > 0) then
c a l l o p e n d a t a f i l e ( out un i t , ” o b j f u n c t i o n . txt ”)
c a l l s ave a r ray 1d ( out un i t , ” va l ” , n b , v a l g r i d )
c a l l s ave a r ray 1d ( out un i t , ” b g r i d ” , n b , b g r i d )
c a l l c l o s e d a t a f i l e ( ou t un i t )
end i f
! s o l v e f o r optimal b ’
b n s o l i d x = maxloc ( v a l g r i d , dim=1 )
! save s o l u t i o n
s o l%b n s o l i d x = b n s o l i d x
s o l%bn so l = b gr id ( b n s o l i d x )
s o l%va l = v a l g r i d ( b n s o l i d x )
s o l%c s o l = ca lc consumpt ion ( n b , n y , i b , i y , i h ,&
i t , bn so l i dx , def , b gr id , y gr id , q , pm)
end subrout ine s o l v e g r i d s e a r c h
164
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine c a l c b o n d p r i c e s c h e d u l e
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗subrout ine c a l c b o n d p r i c e s c h e d u l e ( n b , n y , vnd0 , vd0 ,&
Py cdf , pm, q , p d , y s ta r )
i m p l i c i t none
in t ege r , i n t e n t ( in ) : : n b , n y
r e a l ( 8 ) , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( in ) : : vnd0
! v nd (b , y , h , type ) , va lue o f not d e f a u l t i n g
r e a l ( 8 ) , dimension ( n y , 2 , 2 ) , i n t e n t ( in ) : : vd0
! v d (y , h , type ) , va lue o f d e f a u l t
r e a l ( 8 ) , dimension ( n y , n y ) , i n t e n t ( in ) : : Py cdf
! Py cdf (y , y ’ ) , cd f o f p r o b a b i l i t y t r a n s i t i o n matrix
type ( params ) , i n t e n t ( in ) : : pm
! p o l i c y f u n c t i o n s ( output )
r e a l ( 8 ) , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( out ) : : q
! q (b ’ , y , d , type ’ ) , q schedu le
r e a l ( 8 ) , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( out ) : : p d
! p d (b ’ , y , h ’ , type ’ ) , d e f a u l t p r o b a b i l i t y
in t ege r , dimension ( n b , 2 , 2 ) , i n t e n t ( out ) : : y s ta r
! y∗(b ’ , h ’ , type ’ ) , d e f a u l t t h r e s h o l d s
i n t e g e r : : y s
i n t e g e r : : i bn , i hn , i tn , i t , i y
i n t e g e r : : i t o t h e r
l o g i c a l : : y s f ound
r e a l (8 ) : : pd val
r e a l (8 ) : : pd curr , pd other , p i turn , q va l
! −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−! f i r s t , compute d e f a u l t t h r e s h o l d s and d e f a u l t p r o b a b i l i t i e s
! −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
do i t n = 1 ,2 ! type ’ ( tomorrow ’ s type )
do i hn = 1 ,2 ! h ’ ( h i s t o r y tomorrow )
do i bn = 1 , n b ! b ’ ( debt tomorrow )
165
! Find y∗ such that
! country does NOT DEFAULT f o r y >= y∗! country does DEFAULT f o r y < y∗ ( or y <= y∗−1)
! i f y∗ == 1 , then country doesn ’ t d e f a u l t f o r any y
! i f y∗ = n y + 1 , then country d e f a u l t s f o r a l l y
y s = 0
y s found = . f a l s e .
do whi l e ( . not . y s found )
y s = y s + 1
! check whether country does NOT DEFAULT f o r t h i s y
i f ( vnd0 ( i bn , y s , i hn , i t n ) >= &
vd0 ( y s , i hn , i t n ) ) then
y s found = . t rue .
e l s e i f ( y s == n y ) then
! only reach t h i s i f
! vnd0 (b ’ , y ’ , h ’ , type ’ ) < vd0 (y ’ , h ’ , type ’ ) f o r a l l y ’
y s found = . t rue .
y s = n y + 1
end i f
end do
! save d e f a u l t th r e sho ld
ys ta r ( i bn , i hn , i t n ) = y s
! compute d e f a u l t p r o b a b i l i t i e s
do i y = 1 , n y
i f ( y s == 1) then
pd val = 0d+0
e l s e i f ( y s == n y + 1) then
pd val = 1 .0 d+0
e l s e
pd val = Py cdf ( i y , y s−1)
end i f
p d ( i bn , i y , i hn , i t n ) = pd val
166
end do ! cur rent y loop
end do
end do
end do
! −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−! second , compute bond p r i c e schedu le
! −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
do i t = 1 ,2 ! type TODAY
do i hn = 1 ,2 ! d , d e f a u l t d e c i s i o n TODAY ( i . e . , h ’ )
do i y = 1 , n y ! y , cur r ent y
do i bn = 1 , n b ! b ’ , next per iod ’ s debt cho i c e
! get index f o r other type
i f ( i t == 1) then
i t o t h e r = 2
! other type i s the high type
p i t u rn = pm%piL / 0 . 9 ! prob o f turnover
e l s e
i t o t h e r = 1
! other type i s the low type
p i t u rn = pm%piH /0 .4 ! prob o f turnover
end i f
! cu r r ent type ’ s d e f a u l t p r o b a b i l i t y
pd curr = p d ( i bn , i y , i hn , i t )
! o ther type ’ s d e f a u l t p r o b a b i l i t y
pd other = p d ( i bn , i y , i hn , i t o t h e r )
! compute bond p r i c e
q va l = 1 − p i t u rn ∗ pd other − (1−p i t u rn )&
∗ pd curr
q va l = q va l / (1 + pm%r )
! save p r i c e
q ( i bn , i y , i hn , i t ) = q va l
167
end do
end do
end do
end do
end subrout ine c a l c b o n d p r i c e s c h e d u l e
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine c a l c c v
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗subrout ine c a l c c v ( n b , n y , v0 , vhat0 , Py , pm, cv )
i m p l i c i t none
in t ege r , i n t e n t ( in ) : : n b , n y
r e a l ( 8 ) , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( in ) : : v0
! v (b , y , h , type ) , va lue o f gov ’ t in power
r e a l ( 8 ) , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( in ) : : vhat0
! vhat (b , y , h , type ) , va lue o f gov ’ t out o f power
r e a l ( 8 ) , dimension ( n y , n y ) , i n t e n t ( in ) : : Py
! Py(y , y ’ ) , p r o b a b i l i t y t r a n s i t i o n matrix
type ( params ) , i n t e n t ( in ) : : pm
! p o l i c y f u n c t i o n s ( output )
r e a l ( 8 ) , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( out ) : : cv
! cv (b ’ , y , d , type ) , cont inuat i on va lue s
! l o c a l array
r e a l ( 8 ) , dimension ( n y ) : : vnext
r e a l ( 8 ) , dimension (2 ) : : p i g r i d
i n t e g e r : : i bn , i y , i d , i t
r e a l (8 ) : : cv va l , p i t u rn
p i g r i d (1 ) = pm%piL / 0 . 9 ;
p i g r i d (2 ) = pm%piH / 0 . 4 ;
do i t = 1 ,2 ! cur r ent type , TODAY
do i d = 1 ,2
! d e f a u l t dec i s i on , TODAY (= h i s t o r y tomorrow )
168
do i y = 1 , n y ! output y , TODAY
do i bn = 1 , n b ! b ’ cho i c e
! next per iod :
! with prob . pi , type i t w i l l be out o f power−−r e c e i v e vhat0
! with prob . 1−pi , type i t w i l l s t i l l be in power−r e c e i v e v0
vnext = p i g r i d ( i t ) ∗ vhat0 ( i bn , : , i d ,&
i t ) +(1−p i g r i d ( i t ) ) ∗ v0 ( i bn , : , i d , i t )
! compute cont inuat i on value
cv va l = DOT PRODUCT( Py( i y , : ) , vnext )
! save value
cv ( i bn , i y , i d , i t ) = cv va l
end do
end do
end do
end do
end subrout ine c a l c c v
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine s a v e v f i r e s u l t s
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗subrout ine s a v e v f i r e s u l t s ( n b , n y , b gr id , y gr id , v,&
vnd , vd , vhat , d po l i cy , c p o l i c y , q , bn po l i cy )
i m p l i c i t none
in t ege r , i n t e n t ( in ) : : n b , n y
r e a l ( 8 ) , dimension ( n b ) , i n t e n t ( in ) : : b g r i d
r e a l ( 8 ) , dimension ( n y ) , i n t e n t ( in ) : : y g r i d
r e a l ( 8 ) , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( in ) : : v
r e a l ( 8 ) , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( in ) : : vnd
r e a l ( 8 ) , dimension ( n y , 2 , 2 ) , i n t e n t ( in ) : : vd
r e a l ( 8 ) , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( in ) : : vhat
l o g i c a l , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( in ) : : d p o l i c y
r e a l ( 8 ) , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( in ) : : c p o l i c y
r e a l ( 8 ) , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( in ) : : bn po l i cy
r e a l ( 8 ) , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( in ) : : q
169
! l o c a l v a r i a b l e s
i n t e g e r : : v f i o u t = 232
! save r e s u l t s
c a l l o p e n d a t a f i l e ( v f i o u t , ” r e s u l t s / v f i d a t a . txt ” ) ;
c a l l s ave a r ray 1d ( v f i o u t , ” b g r i d ” , n b , b g r i d )
c a l l s ave a r ray 1d ( v f i o u t , ” y g r i d ” , n y , y g r i d )
c a l l s ave a r ray 4d ( v f i o u t , ”v ” , n b , n y , 2 , 2 , v )
c a l l s ave a r ray 4d ( v f i o u t , ”vnd ” , n b , n y , 2 , 2 , vnd )
c a l l s ave a r ray 3d ( v f i o u t , ”vd ” , n y , 2 , 2 , vd )
c a l l s ave a r ray 4d ( v f i o u t , ”vhat ” , n b , n y , 2 , 2 , vhat )
c a l l s ave a r ray 4d ( v f i o u t , ”d” , n b , n y , 2 , 2 , d p o l i c y )
c a l l s ave a r ray 4d ( v f i o u t , ”c ” , n b , n y , 2 , 2 , c p o l i c y )
c a l l s ave a r ray 4d ( v f i o u t , ”q ” , n b , n y , 2 , 2 , q )
c a l l s ave a r ray 4d ( v f i o u t , ”bn” , n b , n y , 2 , 2 , bn po l i cy )
c a l l c l o s e d a t a f i l e ( v f i o u t )
! save v , vnd , vd , vhat in s epara t e f i l e s
open ( un i t=v f i o u t , f i l e =” r e s u l t s / guess v0 . txt ” , a c t i on=&
” wr i t e ” , s t a t u s=”r e p l a c e ”)
wr i t e ( v f i o u t , ∗ ) v
c l o s e ( v f i o u t )
open ( un i t=v f i o u t , f i l e =” r e s u l t s / guess vnd0 . txt ” , a c t i on=&
” wr i t e ” , s t a t u s=”r e p l a c e ”)
wr i t e ( v f i o u t , ∗ ) vnd
c l o s e ( v f i o u t )
open ( un i t=v f i o u t , f i l e =” r e s u l t s / guess vd0 . txt ” , a c t i on=&
” wr i t e ” , s t a t u s=”r e p l a c e ”)
wr i t e ( v f i o u t , ∗ ) vd
c l o s e ( v f i o u t )
open ( un i t=v f i o u t , f i l e =” r e s u l t s / guess vhat0 . txt ” , &
ac t i on=”wr i t e ” , s t a t u s=”r e p l a c e ”)
170
wr i t e ( v f i o u t , ∗ ) vhat
c l o s e ( v f i o u t )
end subrout ine s a v e v f i r e s u l t s
end module v f i module
171
Listing A.3: Simulation of Model
module sim module
use mode l too l s
i m p l i c i t none
conta in s
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine s imulate
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗subrout ine s imulate ( n b , n y , b gr id , y gr id , Py cdf , &
mu y cdf , Pt , Pt cdf , mu t cdf , q , p d , d po l i cy , &
c p o l i c y , bn po l i cy , bn idx po l i cy , pm)
i m p l i c i t none
in t ege r , i n t e n t ( in ) : : n b , n y
r e a l ( 8 ) , dimension ( n b ) , i n t e n t ( in ) : : b g r i d
r e a l ( 8 ) , dimension ( n y ) , i n t e n t ( in ) : : y g r i d
r e a l ( 8 ) , dimension ( n y , n y ) , i n t e n t ( in ) : : Py cdf
r e a l ( 8 ) , dimension ( n y ) , i n t e n t ( in ) : : mu y cdf
r e a l ( 8 ) , dimension ( 2 , 2 ) , i n t e n t ( in ) : : Pt
r e a l ( 8 ) , dimension ( 2 , 2 ) , i n t e n t ( in ) : : Pt cd f
r e a l ( 8 ) , dimension ( 2 ) , i n t e n t ( in ) : : mu t cdf
r e a l ( 8 ) , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( in ) : : q
r e a l ( 8 ) , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( in ) : : p d
l o g i c a l , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( in ) : : d p o l i c y
r e a l ( 8 ) , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( in ) : : c p o l i c y
r e a l ( 8 ) , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( in ) : : bn po l i cy
in t ege r , dimension ( n b , n y , 2 , 2 ) , i n t e n t ( in ) : : b n i d x p o l i c y
type ( params ) , i n t e n t ( in ) : : pm
! l o c a l a r rays (make a l l o c a t a b l e to avoid memory problems )
in t ege r , a l l o c a t a b l e , dimension ( : , : ) : : s im type
! s imulated type ( = 1 , low type , = 2 , high type )
in t ege r , a l l o c a t a b l e , dimension ( : , : ) : : s im y
! t h i s i s j u s t the index f o r output
r e a l ( 8 ) , a l l o c a t a b l e , dimension ( : , : ) : : s im output
172
! t h i s i s a c tua l s imulated output
r e a l ( 8 ) , a l l o c a t a b l e , dimension ( : , : ) : : s im b
! s imulated b ’
in t ege r , a l l o c a t a b l e , dimension ( : , : ) : : s im b idx
! s imulated b cho i c e ( index )
in t ege r , a l l o c a t a b l e , dimension ( : , : ) : : s im h
! s imulated h i s t o r y ( =1 i f no d e f a u l t prev per iod , . .
!=2 i f d e f a u l t )
l o g i c a l , a l l o c a t a b l e , dimension ( : , : ) : : s im d
! s imulated d e f a u l t d e c i s i o n
r e a l ( 8 ) , a l l o c a t a b l e , dimension ( : , : ) : : s im c
! s imulated consumption
r e a l ( 8 ) , a l l o c a t a b l e , dimension ( : , : ) : : sim bn
! s imulated b ’ cho i c e
in t ege r , a l l o c a t a b l e , dimension ( : , : ) : : s im bn idx
! s imulated b ’ cho i c e ( index )
r e a l ( 8 ) , a l l o c a t a b l e , dimension ( : , : ) : : sim pd
! s imulated d e f a u l t p r o b a b i l i t y
r e a l ( 8 ) , a l l o c a t a b l e , dimension ( : , : ) : : s im q
! s imulated bond p r i c e
i n t e g e r : : n samples , n pe r i od s
i n t e g e r : : i , t
i n t e g e r : : i b , i y , i h , i t ! cu r r ent s t a t e
i n t e g e r : : i bn , i d ! cur r ent c h o i c e s
l o g i c a l : : de f
i n t e g e r : : s im out = 123
n samples = pm%n samples ! number o f samples in s imu la t i on
n pe r i od s = pm%n per i od s
! number o f pe r i od s f o r each sample in s imu la t i on
! a l l o c a t e memory
a l l o c a t e ( s im type ( n per iods , n samples ) , s im y ( n per iods ,&
n samples ) , s im output ( n per iods , n samples ) )
a l l o c a t e ( sim b ( n per iods , n samples ) , s im b idx ( n per iods ,&
n samples ) , s im h ( n per iods , n samples ) )
a l l o c a t e ( sim d ( n per iods , n samples ) , s im c ( n per iods , &
173
n samples ) , sim bn ( n per iods , n samples ) )
a l l o c a t e ( s im bn idx ( n per iods , n samples ) , s im q ( n per iods ,&
n samples ) , sim pd ( n per iods , n samples ) )
do i = 1 , n samples
! s imulate types ( a l l at once ) f o r t h i s sample
c a l l gen shocks ( n per iods , 2 , mu t cdf , Pt cdf ,&
s im type ( : , i ) )
! s imulate y ( a l l at once ) f o r t h i s sample
c a l l gen shocks ( n per iods , n y , mu y cdf , Py cdf ,&
sim y ( : , i ) )
! i n i t i a l i z e p o l i c y c h o i c e s
i bn = n b ! max b ’
i d = 1 ! no d e f a u l t
do t = 1 , n pe r i od s
! update i n i t i a l s t a t e from c h o i c e s l a s t per iod
i b = i bn
i h = i d
! update i n i t i a l s t a t e f o r output and type
i t = sim type ( t , i )
i y = sim y ( t , i )
! save s t a t e
sim h ( t , i ) = i h
s im b idx ( t , i ) = i b
sim b ( t , i ) = b gr id ( i b )
s im output ( t , i ) = exp ( y g r i d ( i y ) )
! p o l i c y c h o i c e s
i bn = b n i d x p o l i c y ( i b , i y , i h , i t )
de f = d p o l i c y ( i b , i y , i h , i t )
i f ( de f ) then
i d = 2
e l s e
174
i d = 1
end i f
! save p o l i c y c h o i c e s
sim d ( t , i ) = de f
s im c ( t , i ) = c p o l i c y ( i b , i y , i h , i t )
sim bn ( t , i ) = bn po l i cy ( i b , i y , i h , i t )
s im bn idx ( t , i ) = i bn
! bond pr i ce , g iven p o l i c y c h o i c e s
sim q ( t , i ) = q ( i bn , i y , i d , i t )
! d e f a u l t p robab i l i t y , g iven p o l i c y c h o i c e s
! p d g i v e s the p r o b a b i l i t y o f de fau l t , g iven the
! type in gov ’ t tomorrow
sim pd ( t , i ) = DOT PRODUCT( Pt ( i t , : ) , p d ( i bn ,&
i y , i d , : ) )
end do
i f (mod( i , 10) == 1) then
p r i n t ∗ , ” sample = ” , i
end i f
end do
! −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−! save s imu la t i on r e s u l t s
! −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
pr in t ∗ , ”∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗”p r i n t ∗ , ” Saving Simulat ion Resu l t s ”
p r i n t ∗ , ”∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗”
c a l l o p e n d a t a f i l e ( sim out , ” r e s u l t s / s im data . txt ” ) ;
c a l l s ave a r ray 2d ( sim out , ” s im type ” , n per iods , &
n samples , s im type )
c a l l s ave a r ray 2d ( sim out , ” s im output ” , n per iods ,&
175
n samples , s im output )
c a l l s ave a r ray 2d ( sim out , ” sim b ” , n per iods , n samples&
, sim b )
c a l l s ave a r ray 2d ( sim out , ” sim bn ” , n per iods , n samples ,&
sim bn )
c a l l s ave a r ray 2d ( sim out , ” sim q ” , n per iods , n samples ,&
sim q )
c a l l s ave a r ray 2d ( sim out , ” sim pd ” , n per iods , n samples ,&
sim pd )
c a l l s ave a r ray 2d ( sim out , ” sim d ” , n per iods , n samples ,&
sim d )
c a l l s ave a r ray 2d ( sim out , ” s im c ” , n per iods , n samples ,&
s im c )
c a l l c l o s e d a t a f i l e ( s im out )
end subrout ine s imulate
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine gen shocks
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗subrout ine gen shocks ( n per iods , num shocks , mu cdf , &
P cdf , s im shock )
in t ege r , i n t e n t ( in ) : : n per iods , num shocks
r e a l ( 8 ) , dimension ( num shocks ) , i n t e n t ( in ) : : mu cdf
r e a l ( 8 ) , dimension ( num shocks , num shocks ) , i n t e n t ( in ) : : &
P cdf
in t ege r , dimension ( n pe r i od s ) , i n t e n t ( out ) : : s im shock
r e a l ( 8 ) , a l l o c a t a b l e , dimension ( : ) : : u
i n t e g e r : : t
! a l l o c a t e memory f o r u
a l l o c a t e (u( n pe r i od s ) )
! generate random v ar i a b l e s , which i s uni formly
! d i s t r i b u t e d [ 0 , 1 )
c a l l RANDOMNUMBER(u)
176
! f i r s t c a l c u a l t e i n i t i a l type
s im shock (1 ) = ca lc markov shock f rom uni fo rm rv (u ( 1 ) , &
num shocks , mu cdf )
! now determine types f o r a l l f u tu r e pe r i od s
do t = 2 , n pe r i od s
s im shock ( t ) = ca lc markov shock f rom uni fo rm rv ( &
u( t ) , num shocks , P cdf ( s im shock ( t −1) , : ) )
end do
d e a l l o c a t e (u)
end subrout ine gen shocks
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! f unc t i on ca l c markov shock f rom uni fo rm rv
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗f unc t i on ca l c markov shock f rom uni fo rm rv (u , n , P cdf )&
r e s u l t ( j )
i m p l i c i t none
r e a l ( 8 ) , i n t e n t ( in ) : : u
in t ege r , i n t e n t ( in ) : : n
r e a l ( 8 ) , dimension (n ) , i n t e n t ( in ) : : P cdf
i n t e g e r : : j ! output
! l o c a l v a r i a b l e s
l o g i c a l : : done
done = . f a l s e .
j = 0
! u i s uni formly d i s t r i b u t e d over [ 0 , 1 )
! convert i t i n to an index f o r p ro duc t i v i t y
! us ing the cumulat ive p r o b a b i l i t y t r a n s i t i o n matrix
do whi l e ( . not . done )
j = j + 1 ;
! stop i f u < P cdf ( j )
177
! u has to be l e s s than 1
! P cdf (n) == 1 , so even tua l l y t h i s w i l l be t rue
done = (u < P cdf ( j ) ) ;
end do
end func t i on ca l c markov shock f rom uni fo rm rv
end module sim module
178
Listing A.4: Main Program: Driver for Iteration and Simulation
program corrupt ion mode l
use mode l too l s
use gr id module
use v f i module
use sim module
i m p l i c i t none
! Var i ab l e s
type ( params ) : : pm
r e a l ( 8 ) , a l l o c a t a b l e , dimension ( : ) : : b g r i d
! b g r id po in t s
r e a l ( 8 ) , a l l o c a t a b l e , dimension ( : ) : : y g r i d
! y g r id po in t s
r e a l ( 8 ) , a l l o c a t a b l e , dimension ( : , : ) : : Py
! prob t r a n s i t i o n matrix f o r y
r e a l ( 8 ) , a l l o c a t a b l e , dimension ( : , : ) : : Py cdf
! prob t r a n s i t i o n matrix f o r y , cd f
r e a l ( 8 ) , a l l o c a t a b l e , dimension ( : ) : : mu y
! inv d i s t r i b u t i o n f o r y
r e a l ( 8 ) , a l l o c a t a b l e , dimension ( : ) : : mu y cdf
! inv d i s t r i b u t i o n f o r y , cd f
r e a l ( 8 ) , a l l o c a t a b l e , dimension ( : , : ) : : Pt
! prob t r a n s i t i o n matrix , government type
r e a l ( 8 ) , a l l o c a t a b l e , dimension ( : , : ) : : Pt cd f
! prob t r a n s i t i o n matrix , government type , cd f
r e a l ( 8 ) , a l l o c a t a b l e , dimension ( : ) : : mu t
! inv d i s t r i b u t i o n f o r government type
r e a l ( 8 ) , a l l o c a t a b l e , dimension ( : ) : : mu t cdf
! inv d i s t r i b u t i o n f o r government type , cd f
r e a l ( 8 ) , a l l o c a t a b l e , dimension ( : , : , : , : ) : : q
! q (b ’ , y , d , type ) , q schedu le
r e a l ( 8 ) , a l l o c a t a b l e , dimension ( : , : , : , : ) : : p d
! p d (b ’ , y , h ’ , type ’ ) , d e f a u l t p r o b a b i l i t y
179
i n t ege r , a l l o c a t a b l e , dimension ( : , : , : ) : : y s ta r
! y∗(b ’ , h ’ , type ’ ) , d e f a u l t t h r e s h o l d s
l o g i c a l , a l l o c a t a b l e , dimension ( : , : , : , : ) : : d p o l i c y
! d (b , y , h i s t , type ) , d e f a u l t p o l i c y
r e a l ( 8 ) , a l l o c a t a b l e , dimension ( : , : , : , : ) : : c p o l i c y
! c (b , y , h i s t , type ) , consumption p o l i c y
r e a l ( 8 ) , a l l o c a t a b l e , dimension ( : , : , : , : ) : : bn po l i cy
! b ’ ( b , y , h i s t , type ) , debt p o l i c y
in t ege r , a l l o c a t a b l e , dimension ( : , : , : , : ) : : b n i d x p o l i c y
! b ’ ( b , y , h i s t , type ) , debt p o l i c y ( index )
i n t e g e r : : n b , n y
!%%%%% Load parameters
! load parameters
c a l l l oad parameter s (” input params . txt ” , pm)
n b = pm%n b
n y = pm%n y
! save parameters i n to a format that w i l l be e a s i e r . .
! to read in Matlab
c a l l save parameters (pm)
!%%%%% Al lo ca t e memory
! to avoid memory problems , a r rays made a l l o c a t a b l e . . .
! and memory e x p l i c i t l y a l l o c a t e d
a l l o c a t e ( b g r i d ( n b ) , y g r i d ( n y ) )
a l l o c a t e ( Py( n y , n y ) , Py cdf ( n y , n y ) , mu y( n y ) ,&
mu y cdf ( n y ) )
a l l o c a t e ( Pt ( 2 , 2 ) , Pt cd f ( 2 , 2 ) , mu t ( 2 ) , mu t cdf (2 ) )
a l l o c a t e ( q ( n b , n y , 2 , 2 ) , p d ( n b , n y , 2 , 2 ) , d p o l i c y&
( n b ,&n y , 2 , 2 ) , c p o l i c y ( n b , n y , 2 , 2 ) )
a l l o c a t e ( bn po l i cy ( n b , n y , 2 , 2 ) , b n i d x p o l i c y ( n b ,&
n y , 2 , 2 ) )
a l l o c a t e ( y s ta r ( n b , 2 , 2 ) )
!%%%%% Construct g r i d s
180
c a l l c o n s t r u c t g r i d s (pm, b gr id , y gr id , Py , Py cdf ,&
mu y , mu y cdf , Pt , Pt cdf , mu t , mu t cdf )
p r i n t ∗ , ”∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗”p r i n t ∗ , ”Value Function I t e r a t i o n ”
p r i n t ∗ , ”∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗”
!%%%%% Value Function I t e r a t i o n
c a l l v a l f c n i t e r ( n b , n y , b gr id , y gr id , Py , Py cdf ,&
pm, q , p d , ystar , d po l i cy , c p o l i c y , bn po l i cy , &
b n i d x p o l i c y )
p r i n t ∗ , ”∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗”p r i n t ∗ , ” S imulat ion ”
p r i n t ∗ , ”∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗”
!%%%%% Simulat ion
c a l l s imulate ( n b , n y , b gr id , y gr id , Py cdf ,&
mu y cdf , Pt , Pt cdf , mu t cdf , q , p d , d po l i cy ,&
c p o l i c y , bn po l i cy , bn idx po l i cy , pm)
p r i n t ∗ , ”∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗”p r i n t ∗ , ”Program Done”
p r i n t ∗ , ”∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗”
end program corrupt ion mode l
181
Listing A.5: Grid Construction
module gr id module
use mode l too l s
use a r r a y t o o l s
i m p l i c i t none
conta in s
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine c o n s t r u c t g r i d s
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗subrout ine c o n s t r u c t g r i d s (pm, b gr id , y gr id , Py , &
Py cdf , mu y , mu y cdf , Pt , Pt cdf , mu t , mu t cdf )
i m p l i c i t none
type ( params ) , i n t e n t ( in ) : : pm
r e a l ( 8 ) , dimension (pm%n b ) , i n t e n t ( out ) : : b g r i d
r e a l ( 8 ) , dimension (pm%n y ) , i n t e n t ( out ) : : y g r i d
r e a l ( 8 ) , dimension (pm%n y ,pm%n y ) , i n t e n t ( out ) : : Py
r e a l ( 8 ) , dimension (pm%n y ,pm%n y ) , i n t e n t ( out ) : : Py cdf
r e a l ( 8 ) , dimension (pm%n y ) , i n t e n t ( out ) : : mu y
r e a l ( 8 ) , dimension (pm%n y ) , i n t e n t ( out ) : : mu y cdf
r e a l ( 8 ) , dimension ( 2 , 2 ) , i n t e n t ( out ) : : Pt
r e a l ( 8 ) , dimension ( 2 , 2 ) , i n t e n t ( out ) : : Pt cd f
r e a l ( 8 ) , dimension ( 2 ) , i n t e n t ( out ) : : mu t
r e a l ( 8 ) , dimension ( 2 ) , i n t e n t ( out ) : : mu t cdf
! l o c a l a r rays
r e a l ( 8 ) , dimension (pm%n y−1) : : y mid
! l o c a l v a r i a b l e s
i n t e g e r : : n b , n y
i n t e g e r : : i , j
r e a l (8 ) : : y mean
! need to d e c l a r e alnorm func t i on ( conta ined in asa066 . f90 )
r e a l (8 ) : : alnorm ! c a l c u l a t e s normal cd f
182
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
! get number o f g r i d dpo ints
n b = pm%n b
n y = pm%n y
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! c on s t ruc t g r id po in t s f o r a s s e t s
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗c a l l expspace ( n b , pm%b sca l e , pm%b min , pm%b max , b g r i d )
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! c on s t ruc t g r id po in t s f o r endowment , y
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
c a l l l i n s p a c e ( n y , pm%y min , pm%y max , y g r i d ) ;
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! c on s t ruc t tauchen approximation f o r endowment proce s s
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
! c on s t ruc t midpoint o f g r id po in t s
do i = 1 , n y−1
y mid ( i ) = 0 . 5∗ ( y g r i d ( i ) + y g r i d ( i +1))
end do
! cons t ruc t Tauchen approximation f o r p r o b a b i l i t y . .
! t r a n s i t i o n matrix
do i = 1 , n y
! mean o f endowment proce s s
y mean = (1−pm%rho )∗pm%mean y + pm%rho ∗ y g r i d ( i )
! us ing f a l s e input , alnorm re tu rn s normal cd f
Py( i , 1 ) = alnorm ( ( y mid (1 ) − y mean ) / pm%sigma e &
, . f a l s e . ) ;
! us ing t rue input , alnorm re tu rn s 1 − cd f
183
Py( i , n y ) = alnorm ( ( y mid ( n y−1) − y mean ) / pm%sigma e&
, . t rue . ) ;
! compute p r o b a b i l i t i e s f o r remaining g r id po in t s
do j = 2 , n y−1
Py( i , j ) = alnorm ( ( y mid ( j ) − y mean )/pm%sigma e , &
. f a l s e . ) − alnorm ( ( y mid ( j−1) − y mean)/&
pm%sigma e , . f a l s e . )
end do
end do
! cons t ruc t cd f f o r p r o b a b i l i t y t r a n s i t i o n matrix
Py cdf = cumsum( Py , dim=2 )
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! c on s t ruc t i n v a r i a n t d i s t r i b u t i o n f o r y
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗c a l l c a l c i n v d i s t ( n y , Py , mu y , mu y cdf )
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! c on s t ruc t p r o b a b i l i t y t r a n s i t i o n matrix f o r
! the type o f government
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
! c on s t ruc t p r o b a b i l i t y t r a n s i t i o n matrix
Pt (1 , 1 ) = 1−pm%piL / 0 . 9 ; Pt (1 , 2 ) = pm%piL / 0 . 9 ;
Pt (2 , 1 ) = pm%piH / 0 . 4 ; Pt (2 , 2 ) = 1−pm%piH / 0 . 4 ;
! c ons t ruc t cd f f o r prob t r a n s i t i o n matrix
Pt cd f = cumsum( Pt , dim=2 )
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! c on s t ruc t i n v a r i a n t d i s t r i b u t i o n f o r
! government types
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗c a l l c a l c i n v d i s t (2 , Pt , mu t , mu t cdf )
end subrout ine c o n s t r u c t g r i d s
184
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine c a l c i n v d i s t
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! Compute i n v a r i a n t d i s t r i b u t i o n o f z ’ by i t e r a t i n g on . .
! p r o b a b i l i t y
! t r a n s i t i o n matrix u n t i l convergence .
! Could a l t e r n a t i v e l y c a l c u l a t e t h i s by computing the . .
! e i g e n v e c t o r s
! o f the p r o b a b i l i t y t r a n s i t i o n matrix .
subrout ine c a l c i n v d i s t (n , P, mu, mu cdf )
i m p l i c i t none
in t ege r , i n t e n t ( in ) : : n ! number o f g r id po in t s
r e a l ( 8 ) , dimension (n , n ) , i n t e n t ( in ) : : P
! t r a n s i t i o n matrix
r e a l ( 8 ) , dimension (n ) , i n t e n t ( out ) : : mu
! i n v a r i a n t d i s t r i b u t i o n
r e a l ( 8 ) , dimension (n ) , i n t e n t ( out ) : : mu cdf
! cd f o f i n v a r i a n t d i s t r i b u t i o n
r e a l ( 8 ) , parameter : : TOL = 1.0 e−12
in t ege r , parameter : : MAX ITER = 1000
r e a l (8 ) : : e r r
i n t e g e r : : j , i t e r
l o g i c a l : : done
! l o c a l array
r e a l ( 8 ) , dimension (n) : : mu0
! s o l v e f o r i n v a r i a n t d i s t r i b u t i o n by i t e r a t i n g
! u n t i l i t converges
mu0 = 1 .0
i t e r = 0 ;
done = . f a l s e .
do whi l e ( . not . done )
! compute next per iod ’ s d i s t r i b u t i o n
mu = matmul ( t ranspose (P) , mu0 ) ;
185
! compute convergence e r r o r
e r r = maxval ( abs ( (mu − mu0) / mu0 ) , dim=1 )
! stop i f e r r o r has s u f f i c i e n t l y converged
i f ( e r r < TOL) then
done = . t rue .
end i f
! s top i f maximum i t e r a t i o n s reached
i t e r = i t e r + 1 ;
i f ( i t e r >= MAX ITER) then
done = . t rue .
end i f
! update i n i t i a l d i s t r i b u t i o n
mu0 = mu;
end do
! normal ize d i s t r i b u t i o n
mu = mu / sum(mu)
! Now compute cd f
mu cdf = cumsum(mu)
end subrout ine c a l c i n v d i s t
end module gr id module
186
Listing A.6: Model Tools
module mode l too l s
use data output
i m p l i c i t none
! Def ine s t r u c t u r e to hold parameters
type params
i n t e g e r : : n b
! number o f debt g r id po in t s
i n t e g e r : : n y
! number o f output g r id po in t s
i n t e g e r : : n samples
! number o f samples in s imu la t i on
i n t e g e r : : n pe r i od s
! number o f pe r i od s f o r each sample in s imu la t i on
r e a l (8 ) : : beta ! d i s count f a c t o r
r e a l (8 ) : : sigma ! r i s k ave r s i on
r e a l (8 ) : : r ! r i s k f r e e ra t e
r e a l (8 ) : : rho ! p e r s i s t e n c e o f output
r e a l (8 ) : : s igma e
! std dev o f innovat ion to output
r e a l (8 ) : : lambda ! output l o s s in d e f a u l t
r e a l (8 ) : : tauL ! l e s s cor rupt type , tax
r e a l (8 ) : : tauH ! more corrupt type , tax
r e a l (8 ) : : piL
! p r o b a b i l i t y o f turnover , l e s s cor rupt type
r e a l (8 ) : : piH
! p r o b a b i l i t y o f turnover , more corrupt type
r e a l (8 ) : : b min ! minimum a s s e t l e v e l
r e a l (8 ) : : b max ! maximum a s s e t l e v e l
r e a l (8 ) : : b s c a l e
! c o n t r o l s i n t e r v a l between a s s e t g r id po in t s
r e a l (8 ) : : y width
! ln y in [ mean − width ∗ sd y , mean + width ∗ sd y ]
187
l o g i c a l : : new v0
! i f = 1 , i n i t i a l i z e va l f c n s to 0 , o therwi s e . . .
! load from f i l e s
! de r ived parameters
r e a l (8 ) : : mean y ! mean o f y
r e a l (8 ) : : sd y ! standard dev i a t i on o f y
r e a l (8 ) : : y min
r e a l (8 ) : : y max
end type params
conta in s
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine load parameter s
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗subrout ine load parameter s ( f i l ename , pm)
i m p l i c i t none
cha rac t e r ( l en =∗) , i n t e n t ( in ) : : f i l ename
type ( params ) , i n t e n t ( out ) : : pm
! l o c a l v a r i a b l e s
i n t e g e r : : i n f i l e , new v0 int
i n f i l e = 54
open ( i n f i l e , f i l e = f i l ename )
read ( i n f i l e , ∗ ) pm%n b
read ( i n f i l e , ∗ ) pm%n y
read ( i n f i l e , ∗ ) pm%n samples
read ( i n f i l e , ∗ ) pm%n per i od s
read ( i n f i l e , ∗ ) pm%beta
read ( i n f i l e , ∗ ) pm%sigma
read ( i n f i l e , ∗ ) pm%r
read ( i n f i l e , ∗ ) pm%rho
188
read ( i n f i l e , ∗ ) pm%sigma e
read ( i n f i l e , ∗ ) pm%lambda
read ( i n f i l e , ∗ ) pm%tauL
read ( i n f i l e , ∗ ) pm%tauH
read ( i n f i l e , ∗ ) pm%piL
read ( i n f i l e , ∗ ) pm%piH
read ( i n f i l e , ∗ ) pm%b min
read ( i n f i l e , ∗ ) pm%b max
read ( i n f i l e , ∗ ) pm%b s c a l e
read ( i n f i l e , ∗ ) pm%y width
read ( i n f i l e , ∗ ) new v0 int
rewind ( i n f i l e )
c l o s e ( i n f i l e )
! de r ived parameters
pm%sd y = pm%sigma e / s q r t ( 1 − pm%rho ∗∗2 )
! mean o f y :
! y ’ = (1−rho )∗mean y + rho∗ y + eps
pm%mean y = −0.5 ∗ pm%sigma e ∗∗2
! l i m i t s f o r endowment g r id
pm%y min = pm%mean y − pm%y width ∗ pm%sd y
pm%y max = pm%mean y + pm%y width ∗ pm%sd y
i f ( new v0 int > 0) then
pm%new v0 = . t rue .
e l s e
pm%new v0 = . f a l s e .
end i f
end subrout ine load parameter s
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine save parameters
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗subrout ine save parameters (pm)
i m p l i c i t none
189
type ( params ) , i n t e n t ( in ) : : pm
! l o c a l v a r i a b l e s
i n t e g e r : : param out = 37
! save paramters
c a l l o p e n d a t a f i l e ( param out , ” r e s u l t s /params . txt ” ) ;
c a l l s a v e s c a l a r ( param out , ”n b ” , pm%n b )
c a l l s a v e s c a l a r ( param out , ”n y ” , pm%n y )
c a l l s a v e s c a l a r ( param out , ” n samples ” , pm%n samples )
c a l l s a v e s c a l a r ( param out , ” n pe r i od s ” , pm%n pe r i od s )
c a l l s a v e s c a l a r ( param out , ” beta ” , pm%beta )
c a l l s a v e s c a l a r ( param out , ” sigma ” , pm%sigma )
c a l l s a v e s c a l a r ( param out , ” r ” , pm%r )
c a l l s a v e s c a l a r ( param out , ” rho ” , pm%rho )
c a l l s a v e s c a l a r ( param out , ” s igma e ” , pm%sigma e )
c a l l s a v e s c a l a r ( param out , ”lambda ” , pm%lambda )
c a l l s a v e s c a l a r ( param out , ”tauL ” , pm%tauL )
c a l l s a v e s c a l a r ( param out , ”tauH ” , pm%tauH )
c a l l s a v e s c a l a r ( param out , ”piL ” , pm%piL )
c a l l s a v e s c a l a r ( param out , ”piH ” , pm%piH )
c a l l s a v e s c a l a r ( param out , ”b min ” , pm%b min )
c a l l s a v e s c a l a r ( param out , ”b max ” , pm%b max )
c a l l s a v e s c a l a r ( param out , ” y width ” , pm%y width )
c a l l s a v e s c a l a r ( param out , ”mean y ” , pm%mean y )
c a l l s a v e s c a l a r ( param out , ” sd y ” , pm%sd y )
c a l l s a v e s c a l a r ( param out , ”y min ” , pm%y min )
c a l l s a v e s c a l a r ( param out , ”y max ” , pm%y max )
c a l l c l o s e d a t a f i l e ( param out )
end subrout ine
end module mode l too l s
190
Listing A.7: Data Output
module data output
i m p l i c i t none
i n t e r f a c e s a v e s c a l a r
module procedure s a v e s c a l a r d o u b l e , s a v e s c a l a r i n t ,&
s a v e s c a l a r l o g i c a l
end i n t e r f a c e
i n t e r f a c e save a r ray 1d
module procedure save ar ray 1d doub le , &
s a v e a r r a y 1 d i n t , s a v e a r r a y 1 d l o g i c a l
end i n t e r f a c e
i n t e r f a c e save a r ray 2d
module procedure save ar ray 2d doub le , &
s a v e a r r a y 2 d i n t , s a v e a r r a y 2 d l o g i c a l
end i n t e r f a c e
i n t e r f a c e save a r ray 3d
module procedure save ar ray 3d doub le , s a v e a r r a y 3 d i n t ,&
s a v e a r r a y 3 d l o g i c a l
end i n t e r f a c e
i n t e r f a c e save a r ray 4d
module procedure save ar ray 4d doub le , s a v e a r r a y 4 d i n t ,&
s a v e a r r a y 4 d l o g i c a l
end i n t e r f a c e
conta in s
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine o p e n d a t a f i l e
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! choose any i n t e g e r f o r ou t un i t > 0 , except 6?
subrout ine o p e n d a t a f i l e ( out un i t , f i l ename )
191
i n t ege r , i n t e n t ( in ) : : ou t un i t
cha rac t e r ( l en =∗) , i n t e n t ( in ) : : f i l ename
open ( un i t=out uni t , f i l e=f i l ename , ac t i on=”wr i t e ” , s t a t u s=&
” r e p l a c e ”)
end subrout ine o p e n d a t a f i l e
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine c l o s e d a t a f i l e
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗subrout ine c l o s e d a t a f i l e ( ou t un i t )
i m p l i c i t none
in t ege r , i n t e n t ( in ) : : ou t un i t
c l o s e ( ou t un i t )
end subrout ine c l o s e d a t a f i l e
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine s a v e s c a l a r d o u b l e
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗i m p l i c i t none
in t ege r , i n t e n t ( in ) : : ou t un i t
cha rac t e r ( l en =∗) , i n t e n t ( in ) : : name
r e a l ( 8 ) , i n t e n t ( in ) : : va l
! r ecord d e t a i l s o f v a r i a b l e
! name , # o f dimensions , 1 x 1 array ( i . e . , s c a l a r )
wr i t e ( out un i t , ∗ ) name , ” 2 1 1”
! save value to f i l e
wr i t e ( out un i t , ∗ ) va l
! add an extra space
wr i t e ( out un i t , ∗ ) ””
192
end subrout ine s a v e s c a l a r d o u b l e
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine s a v e s c a l a r i n t
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗subrout ine s a v e s c a l a r i n t ( out un i t , name , va l )
i m p l i c i t none
in t ege r , i n t e n t ( in ) : : ou t un i t
cha rac t e r ( l en =∗) , i n t e n t ( in ) : : name
in t ege r , i n t e n t ( in ) : : va l
! r ecord d e t a i l s o f v a r i a b l e
! name , # o f dimensions , 1 x 1 array ( i . e . , s c a l a r )
wr i t e ( out un i t , ∗ ) name , ” 2 1 1”
! save value to f i l e
wr i t e ( out un i t , ∗ ) va l
! add an extra space
wr i t e ( out un i t , ∗ ) ””
end subrout ine s a v e s c a l a r i n t
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine s a v e s c a l a r l o g i c a l
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗subrout ine s a v e s c a l a r l o g i c a l ( out un i t , name , va l )
i m p l i c i t none
in t ege r , i n t e n t ( in ) : : ou t un i t
cha rac t e r ( l en =∗) , i n t e n t ( in ) : : name
l o g i c a l , i n t e n t ( in ) : : va l
i n t e g e r : : va l ou t
! convert va lue to i n t e g e r
i f ( va l ) then
va l ou t = 1
e l s e
193
va l ou t = 0
end i f
! r ecord d e t a i l s o f v a r i a b l e
! name , # o f dimensions , 1 x 1 array ( i . e . , s c a l a r )
wr i t e ( out un i t , ∗ ) name , ” 2 1 1”
! save value to f i l e
wr i t e ( out un i t , ∗ ) va l ou t
! add an extra space
wr i t e ( out un i t , ∗ ) ””
end subrout ine s a v e s c a l a r l o g i c a l
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine save a r ray 1d doub l e
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗subrout ine save a r ray 1d doub l e ( out un i t , name , n , v a l s )
i m p l i c i t none
in t ege r , i n t e n t ( in ) : : ou t un i t
cha rac t e r ( l en =∗) , i n t e n t ( in ) : : name
in t ege r , i n t e n t ( in ) : : n
r e a l ( 8 ) , dimension (n ) , i n t e n t ( in ) : : v a l s
! r ecord d e t a i l s o f v a r i a b l e
! name , # o f dimensions , n x 1 vec to r
wr i t e ( out un i t , ∗ ) name , ” 2 ” , n , ” 1”
! save array to f i l e
wr i t e ( out un i t , ∗ ) v a l s
! add an extra space
wr i t e ( out un i t , ∗ ) ””
end subrout ine save a r ray 1d doub l e
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
194
! subrout ine s a v e a r r a y 1 d i n t
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗subrout ine s a v e a r r a y 1 d i n t ( out un i t , name , n , v a l s )
i m p l i c i t none
in t ege r , i n t e n t ( in ) : : ou t un i t
cha rac t e r ( l en =∗) , i n t e n t ( in ) : : name
in t ege r , i n t e n t ( in ) : : n
in t ege r , dimension (n ) , i n t e n t ( in ) : : v a l s
! r ecord d e t a i l s o f v a r i a b l e
! name , # o f dimensions , n x 1 vec to r
wr i t e ( out un i t , ∗ ) name , ” 2 ” , n , ” 1”
! save array to f i l e
wr i t e ( out un i t , ∗ ) v a l s
! add an extra space
wr i t e ( out un i t , ∗ ) ””
end subrout ine s a v e a r r a y 1 d i n t
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine s a v e a r r a y 1 d l o g i c a l
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗subrout ine s a v e a r r a y 1 d l o g i c a l ( out un i t , name , n , v a l s )
i m p l i c i t none
in t ege r , i n t e n t ( in ) : : ou t un i t
cha rac t e r ( l en =∗) , i n t e n t ( in ) : : name
in t ege r , i n t e n t ( in ) : : n
l o g i c a l , dimension (n ) , i n t e n t ( in ) : : v a l s
i n t ege r , a l l o c a t a b l e , dimension ( : ) : : v a l s o u t
i n t e g e r : : i
a l l o c a t e ( v a l s o u t (n ) )
! convert to i n t e g e r s
195
! where cons t ruc t can cause s tack over f l ow ? !
! where ( v a l s )
! v a l s o u t = 1
! e l s ewhere
! v a l s o u t = 0
! end where
do i = 1 ,n
i f ( v a l s ( i ) ) then
v a l s o u t ( i ) = 1
e l s e
v a l s o u t ( i ) = 0
end i f
end do
! record d e t a i l s o f v a r i a b l e
! name , # o f dimensions , n x 1 vec to r
wr i t e ( out un i t , ∗ ) name , ” 2 ” , n , ” 1”
! save array to f i l e
wr i t e ( out un i t , ∗ ) v a l s o u t
! add an extra space
wr i t e ( out un i t , ∗ ) ””
d e a l l o c a t e ( v a l s o u t )
end subrout ine s a v e a r r a y 1 d l o g i c a l
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine save a r ray 2d doub l e
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗subrout ine save a r ray 2d doub l e ( out un i t , name , n1 , n2 ,&
v a l s )
i m p l i c i t none
in t ege r , i n t e n t ( in ) : : ou t un i t
cha rac t e r ( l en =∗) , i n t e n t ( in ) : : name
in t ege r , i n t e n t ( in ) : : n1
196
i n t ege r , i n t e n t ( in ) : : n2
r e a l ( 8 ) , dimension ( n1 , n2 ) , i n t e n t ( in ) : : v a l s
! r ecord d e t a i l s o f v a r i a b l e
! name , # o f dimensions , n1 x n2 array
wr i t e ( out un i t , ∗ ) name , ” 2 ” , n1 , n2
! save array to f i l e
wr i t e ( out un i t , ∗ ) v a l s
! add an extra space
wr i t e ( out un i t , ∗ ) ””
end subrout ine save a r ray 2d doub l e
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine s a v e a r r a y 2 d i n t
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗subrout ine s a v e a r r a y 2 d i n t ( out un i t , name , n1 , n2 ,&
v a l s )
i m p l i c i t none
in t ege r , i n t e n t ( in ) : : ou t un i t
cha rac t e r ( l en =∗) , i n t e n t ( in ) : : name
in t ege r , i n t e n t ( in ) : : n1
in t ege r , i n t e n t ( in ) : : n2
in t ege r , dimension ( n1 , n2 ) , i n t e n t ( in ) : : v a l s
! r ecord d e t a i l s o f v a r i a b l e
! name , # o f dimensions , n1 x n2 array
wr i t e ( out un i t , ∗ ) name , ” 2 ” , n1 , n2
! save array to f i l e
wr i t e ( out un i t , ∗ ) v a l s
! add an extra space
wr i t e ( out un i t , ∗ ) ””
end subrout ine s a v e a r r a y 2 d i n t
197
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine s a v e a r r a y 2 d l o g i c a l
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗subrout ine s a v e a r r a y 2 d l o g i c a l ( out un i t , name , n1 , &
n2 , v a l s )
i m p l i c i t none
in t ege r , i n t e n t ( in ) : : ou t un i t
cha rac t e r ( l en =∗) , i n t e n t ( in ) : : name
in t ege r , i n t e n t ( in ) : : n1
in t ege r , i n t e n t ( in ) : : n2
l o g i c a l , dimension ( n1 , n2 ) , i n t e n t ( in ) : : v a l s
i n t ege r , a l l o c a t a b l e , dimension ( : , : ) : : v a l s o u t
i n t e g e r : : i1 , i 2
a l l o c a t e ( v a l s o u t ( n1 , n2 ) )
! convert to i n t e g e r s
! where cons t ruc t caus ing s tack over f l ow ? !
! where ( v a l s )
! v a l s o u t = 1
! e l s ewhere
! v a l s o u t = 0
! end where
do i 2 = 1 , n2
do i 1 = 1 , n1
i f ( v a l s ( i1 , i 2 ) ) then
v a l s o u t ( i1 , i 2 ) = 1
e l s e
v a l s o u t ( i1 , i 2 ) = 0
end i f
end do
end do
! record d e t a i l s o f v a r i a b l e
! name , # o f dimensions , n1 x n2 array
198
wr i t e ( out un i t , ∗ ) name , ” 2 ” , n1 , n2
! save array to f i l e
wr i t e ( out un i t , ∗ ) v a l s o u t
! add an extra space
wr i t e ( out un i t , ∗ ) ””
d e a l l o c a t e ( v a l s o u t )
end subrout ine s a v e a r r a y 2 d l o g i c a l
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine save a r ray 3d doub l e
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗subrout ine save a r ray 3d doub l e ( out un i t , name , n1 , n2 ,&
n3 , v a l s )
i m p l i c i t none
in t ege r , i n t e n t ( in ) : : ou t un i t
cha rac t e r ( l en =∗) , i n t e n t ( in ) : : name
in t ege r , i n t e n t ( in ) : : n1
in t ege r , i n t e n t ( in ) : : n2
in t ege r , i n t e n t ( in ) : : n3
r e a l ( 8 ) , dimension ( n1 , n2 , n3 ) , i n t e n t ( in ) : : v a l s
! r ecord d e t a i l s o f v a r i a b l e
! name , # o f dimensions , n1 x n2 x n3 array
wr i t e ( out un i t , ∗ ) name , ” 3 ” , n1 , n2 , n3
! save array to f i l e
wr i t e ( out un i t , ∗ ) v a l s
! add an extra space
wr i t e ( out un i t , ∗ ) ””
end subrout ine save a r ray 3d doub l e
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
199
! subrout ine s a v e a r r a y 3 d i n t
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗subrout ine s a v e a r r a y 3 d i n t ( out un i t , name , n1 , n2 , &
n3 , v a l s )
i m p l i c i t none
in t ege r , i n t e n t ( in ) : : ou t un i t
cha rac t e r ( l en =∗) , i n t e n t ( in ) : : name
in t ege r , i n t e n t ( in ) : : n1
in t ege r , i n t e n t ( in ) : : n2
in t ege r , i n t e n t ( in ) : : n3
in t ege r , dimension ( n1 , n2 , n3 ) , i n t e n t ( in ) : : v a l s
! r ecord d e t a i l s o f v a r i a b l e
! name , # o f dimensions , n1 x n2 x n3 array
wr i t e ( out un i t , ∗ ) name , ” 3 ” , n1 , n2 , n3
! save array to f i l e
wr i t e ( out un i t , ∗ ) v a l s
! add an extra space
wr i t e ( out un i t , ∗ ) ””
end subrout ine s a v e a r r a y 3 d i n t
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine s a v e a r r a y 3 d l o g i c a l
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗subrout ine s a v e a r r a y 3 d l o g i c a l ( out un i t , name , n1 , n2 , &
n3 , v a l s )
i m p l i c i t none
in t ege r , i n t e n t ( in ) : : ou t un i t
cha rac t e r ( l en =∗) , i n t e n t ( in ) : : name
in t ege r , i n t e n t ( in ) : : n1
in t ege r , i n t e n t ( in ) : : n2
in t ege r , i n t e n t ( in ) : : n3
l o g i c a l , dimension ( n1 , n2 , n3 ) , i n t e n t ( in ) : : v a l s
200
i n t ege r , a l l o c a t a b l e , dimension ( : , : , : ) : : v a l s o u t
i n t e g e r : : i1 , i2 , i 3
a l l o c a t e ( v a l s o u t ( n1 , n2 , n3 ) )
! convert to i n t e g e r s
! where cons t ruc t caus ing s tack over f l ow ? !
! where ( v a l s )
! v a l s o u t = 1
! e l s ewhere
! v a l s o u t = 0
! end where
do i 3 = 1 , n3
do i 2 = 1 , n2
do i 1 = 1 , n1
i f ( v a l s ( i1 , i2 , i 3 ) ) then
v a l s o u t ( i1 , i2 , i 3 ) = 1
e l s e
v a l s o u t ( i1 , i2 , i 3 ) = 0
end i f
end do
end do
end do
! record d e t a i l s o f v a r i a b l e
! name , # o f dimensions , n1 x n2 x n3 array
wr i t e ( out un i t , ∗ ) name , ” 3 ” , n1 , n2 , n3
! save array to f i l e
wr i t e ( out un i t , ∗ ) v a l s o u t
! add an extra space
wr i t e ( out un i t , ∗ ) ””
d e a l l o c a t e ( v a l s o u t )
end subrout ine s a v e a r r a y 3 d l o g i c a l
201
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine save a r ray 4d doub l e
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗subrout ine save a r ray 4d doub l e ( out un i t , name , n1 , n2 ,&
n3 , n4 , v a l s )
i m p l i c i t none
in t ege r , i n t e n t ( in ) : : ou t un i t
cha rac t e r ( l en =∗) , i n t e n t ( in ) : : name
in t ege r , i n t e n t ( in ) : : n1
in t ege r , i n t e n t ( in ) : : n2
in t ege r , i n t e n t ( in ) : : n3
in t ege r , i n t e n t ( in ) : : n4
r e a l ( 8 ) , dimension ( n1 , n2 , n3 , n4 ) , i n t e n t ( in ) : : v a l s
! r ecord d e t a i l s o f v a r i a b l e
! name , # o f dimensions , n1 x n2 x n3 x n4 array
wr i t e ( out un i t , ∗ ) name , ” 4 ” , n1 , n2 , n3 , n4
! save array to f i l e
wr i t e ( out un i t , ∗ ) v a l s
! add an extra space
wr i t e ( out un i t , ∗ ) ””
end subrout ine save a r ray 4d doub l e
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine s a v e a r r a y 4 d i n t
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗subrout ine s a v e a r r a y 4 d i n t ( out un i t , name , n1 , n2 ,&
n3 , n4 , v a l s )
i m p l i c i t none
in t ege r , i n t e n t ( in ) : : ou t un i t
cha rac t e r ( l en =∗) , i n t e n t ( in ) : : name
in t ege r , i n t e n t ( in ) : : n1
in t ege r , i n t e n t ( in ) : : n2
in t ege r , i n t e n t ( in ) : : n3
202
i n t ege r , i n t e n t ( in ) : : n4
in t ege r , dimension ( n1 , n2 , n3 , n4 ) , i n t e n t ( in ) : : v a l s
! r ecord d e t a i l s o f v a r i a b l e
! name , # o f dimensions , n1 x n2 x n3 x n4 array
wr i t e ( out un i t , ∗ ) name , ” 4 ” , n1 , n2 , n3 , n4
! save array to f i l e
wr i t e ( out un i t , ∗ ) v a l s
! add an extra space
wr i t e ( out un i t , ∗ ) ””
end subrout ine s a v e a r r a y 4 d i n t
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine s a v e a r r a y 4 d l o g i c a l
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗subrout ine s a v e a r r a y 4 d l o g i c a l ( out un i t , name , n1 , n2 ,&
n3 , n4 , v a l s )
i m p l i c i t none
in t ege r , i n t e n t ( in ) : : ou t un i t
cha rac t e r ( l en =∗) , i n t e n t ( in ) : : name
in t ege r , i n t e n t ( in ) : : n1
in t ege r , i n t e n t ( in ) : : n2
in t ege r , i n t e n t ( in ) : : n3
in t ege r , i n t e n t ( in ) : : n4
l o g i c a l , dimension ( n1 , n2 , n3 , n4 ) , i n t e n t ( in ) : : v a l s
i n t ege r , a l l o c a t a b l e , dimension ( : , : , : , : ) : : v a l s o u t
i n t e g e r : : i1 , i2 , i3 , i 4
a l l o c a t e ( v a l s o u t ( n1 , n2 , n3 , n4 ) )
! convert to i n t e g e r s
! where cons t ruc t caus ing s tack over f l ow ?
! where ( v a l s )
! v a l s o u t = 1
203
! e l s ewhere
! v a l s o u t = 0
! end where
do i 4 = 1 , n4
do i 3 = 1 , n3
do i 2 = 1 , n2
do i 1 = 1 , n1
i f ( v a l s ( i1 , i2 , i3 , i 4 ) ) then
v a l s o u t ( i1 , i2 , i3 , i 4 ) = 1
e l s e
v a l s o u t ( i1 , i2 , i3 , i 4 ) = 0
end i f
end do
end do
end do
end do
! record d e t a i l s o f v a r i a b l e
! name , # o f dimensions , n1 x n2 x n3 x n4 array
wr i t e ( out un i t , ∗ ) name , ” 4 ” , n1 , n2 , n3 , n4
! save array to f i l e
wr i t e ( out un i t , ∗ ) v a l s o u t
! add an extra space
wr i t e ( out un i t , ∗ ) ””
d e a l l o c a t e ( v a l s o u t )
end subrout ine s a v e a r r a y 4 d l o g i c a l
end module data output
204
Listing A.8: Array Tools
module a r r a y t o o l s
i m p l i c i t none
i n t e r f a c e cumsum
module procedure cumsum matrix , cumsum vector
end i n t e r f a c e
conta in s
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine expspace
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗subrout ine expspace ( n x , x s ca l e , x min , x max , x vec )
i m p l i c i t none
in t ege r , i n t e n t ( in ) : : n x
r e a l ( 8 ) , i n t e n t ( in ) : : x s ca l e , x min , x max
r e a l ( 8 ) , dimension ( n x ) , i n t e n t ( out ) : : x vec
i n t e g e r : : i
r e a l (8 ) : : s t ep
!−−−−!
! c on s t ruc t g r id po in t s
s tep = ( x max − x min )/ r e a l ( n x−1, kind =8)∗∗ x s c a l e
do i =1,n x−1
x vec ( i ) = x min + step ∗( i −1)∗∗ x s c a l e ;
end do
x vec ( n x ) = x max
end subrout ine expspace
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine l i n s p a c e
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
205
subrout ine l i n s p a c e ( n x , x min , x max , x vec )
i m p l i c i t none
in t ege r , i n t e n t ( in ) : : n x
r e a l ( 8 ) , i n t e n t ( in ) : : x min , x max
r e a l ( 8 ) , dimension ( n x ) , i n t e n t ( out ) : : x vec
i n t e g e r : : i
r e a l (8 ) : : s t ep
!−−−−!
! c on s t ruc t g r id po in t s
s tep = ( x max − x min ) / ( ( n x−1))
do i =1,n x
x vec ( i ) = x min + step ∗( i −1);
end do
end subrout ine l i n s p a c e
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine cumsum matrix
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! Cumsum computes the cumulat ive sum .
!
! After c a l l i n g B = cumsum(A, DIM=1)
!B w i l l conta in the cumulat ive sum of A along each column
! After c a l l i n g B = cumsum(A, DIM=2)
! B w i l l conta in the cumulat ive sum of A along each row
func t i on cumsum matrix (A, dim) r e s u l t (B)
i m p l i c i t none
r e a l ( 8 ) , dimension ( : , : ) , i n t e n t ( in ) : : A
in t ege r , i n t e n t ( in ) : : dim
r e a l ( 8 ) , dimension ( s i z e (A, dim=1) , s i z e (A, dim=2)) : : B
i n t e g e r : : i , j
i n t e g e r : : M, N
r e a l (8 ) : : sum val
206
! get dimensions o f A
M = s i z e (A, dim=1) ! number o f rows
N = s i z e (A, dim=2) ! number o f column
i f (dim == 1) then
! sum a c r o s s dimension 1 ( columns )
do j = 1 ,N
! i n i t i a l i z e cumulat ive sum
sum val = 0 . 0 ;
! loop a c r o s s each row o f C
do i = 1 ,M
sum val = sum val + A( i , j ) ;
B( i , j ) = sum val ;
end do
end do
e l s e i f ( dim == 2) then
! sum a c r o s s dimension 2 ( rows )
! loop a c r o s s each row o f C
do i = 1 ,M
! i n i t i a l i z e cumulat ive sum
sum val = 0 . 0 ;
! loop a c r o s s each column o f C
do j = 1 ,N
sum val = sum val + A( i , j ) ;
B( i , j ) = sum val ;
end do
end do
e l s e
! e r r o r
end i f
end func t i on cumsum matrix
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗
207
! subrout ine cumsum vector
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! Cumsum computes the cumulat ive sum .
!
! After c a l l i n g B = cumsum(A)
! B w i l l conta in the cumulat ive sum of A
func t i on cumsum vector (A) r e s u l t (B)
i m p l i c i t none
r e a l ( 8 ) , dimension ( : ) , i n t e n t ( in ) : : A
r e a l ( 8 ) , dimension ( s i z e (A) ) : : B
i n t e g e r : : i , N
! get dimensions o f A
N = s i z e (A) ! number o f e lements in A
! c a l c u l a t e cumulat ive sum
i f (N > 0) then
B(1) = A(1)
do i = 2 ,N
B( i ) = B( i −1) + A( i )
end do
end i f
end func t i on cumsum vector
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine s o r t
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! So r t s an array ar r ( 1 : n ) in to ascending numerica l order , , ,
! us ing the Quicksort a lgor i thm . n i s input ; a r r i s r ep l aced . .
! on output by i t s so r t ed rearrangement .
! Parameters : M i s the s i z e o f subarrays so r t ed by s t r a i g h t
! i n s e r t i o n and NSTACK i s the r equ i r ed a u x i l i a r y s to rage .
! Adapted from Numerical Rec ipes in Fortran Book
subrout ine s o r t (n , a r r )
i m p l i c i t none
208
i n t ege r , i n t e n t ( in ) : : n
r e a l ( 8 ) , dimension (n) : : a r r
i n t ege r , parameter : : M = 7
int ege r , parameter : : NSTACK = 50
i n t e g e r : : i , i r , j , j s t ack , k , l
i n t ege r , dimension (NSTACK) : : i s t a c k
r e a l (8 ) : : a , temp
j s t a c k = 0
l = 1
i r = n
1 i f ( i r−l < M) then
do j = l +1, i r
a = ar r ( j )
do i = j −1, l ,−1
i f ( a r r ( i ) <= a ) goto 2
ar r ( i +1) = ar r ( i )
end do
i = l−1
2 ar r ( i +1) = a
end do
i f ( j s t a c k == 0) re turn
i r = i s t a c k ( j s t a c k )
l = i s t a c k ( j s tack −1)
j s t a c k = j s tack−2
e l s e
k = ( l+i r )/2
temp = arr ( k )
a r r ( k ) = ar r ( l +1)
a r r ( l +1) = temp
i f ( a r r ( l ) > ar r ( i r ) ) then
temp = arr ( l )
a r r ( l ) = ar r ( i r )
a r r ( i r ) = temp
end i f
i f ( a r r ( l +1) > ar r ( i r ) ) then
209
temp = arr ( l +1)
a r r ( l +1) = ar r ( i r )
a r r ( i r ) = temp
end i f
i f ( a r r ( l ) > ar r ( l +1)) then
temp = arr ( l )
a r r ( l ) = ar r ( l +1)
a r r ( l +1) = temp
end i f
i = l+1
j = i r
a = ar r ( l +1)
3 cont inue
i = i+1
i f ( a r r ( i ) < a ) goto 3
4 cont inue
j = j−1
i f ( a r r ( j ) > a ) goto 4
i f ( j < i ) goto 5
temp = arr ( i )
a r r ( i ) = ar r ( j )
a r r ( j ) = temp
goto 3
5 ar r ( l +1) = ar r ( j )
a r r ( j ) = a
j s t a c k = j s t a c k + 2
i f ( j s t a c k > NSTACK) pause ’NSTACK too smal l in sort ’
i f ( i r−i+1 >= j−l ) then
i s t a c k ( j s t a c k ) = i r
i s t a c k ( j s tack −1) = i
i r = j−1
e l s e
i s t a c k ( j s t a c k ) = j−1
i s t a c k ( j s tack −1) = l
l = i
end i f
end i f
goto 1
end subrout ine s o r t
210
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! subrout ine so r t 2
!∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗! So r t s an array ar r ( 1 : n ) in to ascending order us ing
! Quicksort , whi l e making the cor re spond ing rearrangement
! o f the array brr ( 1 : n ) .
! Adapted from Numerical Rec ipes in Fortran Book
subrout ine so r t 2 (n , arr , brr )
i m p l i c i t none
in t ege r , i n t e n t ( in ) : : n
r e a l ( 8 ) , dimension (n) : : a r r
i n t ege r , dimension (n) : : brr
in t ege r , parameter : : M = 7
int ege r , parameter : : NSTACK = 50
i n t e g e r : : i , i r , j , j s t ack , k , l
i n t ege r , dimension (NSTACK) : : i s t a c k
r e a l (8 ) : : a , temp
i n t e g e r : : b , tempb
j s t a c k = 0
l = 1
i r = n
1 i f ( i r−l < M) then
do j = l +1, i r
a = ar r ( j )
b = brr ( j )
do i = j −1, l ,−1
i f ( a r r ( i ) <= a ) goto 2
ar r ( i +1) = ar r ( i )
brr ( i +1) = brr ( i )
end do
i = l−1
2 ar r ( i +1) = a
211
brr ( i +1) = b
end do
i f ( j s t a c k == 0) re turn
i r = i s t a c k ( j s t a c k )
l = i s t a c k ( j s tack −1)
j s t a c k = j s tack−2
e l s e
k = ( l+i r )/2
temp = arr ( k )
a r r ( k ) = ar r ( l +1)
a r r ( l +1) = temp
tempb = brr ( k )
brr ( k ) = brr ( l +1)
brr ( l +1) = tempb
i f ( a r r ( l ) > ar r ( i r ) ) then
temp = arr ( l )
a r r ( l ) = ar r ( i r )
a r r ( i r ) = temp
tempb = brr ( l )
brr ( l ) = brr ( i r )
brr ( i r ) = tempb
end i f
i f ( a r r ( l +1) > ar r ( i r ) ) then
temp = arr ( l +1)
a r r ( l +1) = ar r ( i r )
a r r ( i r ) = temp
tempb = brr ( l +1)
brr ( l +1) = brr ( i r )
brr ( i r ) = tempb
end i f
i f ( a r r ( l ) > ar r ( l +1)) then
temp = arr ( l )
a r r ( l ) = ar r ( l +1)
a r r ( l +1) = temp
tempb = brr ( l )
brr ( l ) = brr ( l +1)
brr ( l +1) = tempb
end i f
i = l+1
212
j = i r
a = ar r ( l +1)
b = brr ( l +1)
3 cont inue
i = i+1
i f ( a r r ( i ) < a ) goto 3
4 cont inue
j = j−1
i f ( a r r ( j ) > a ) goto 4
i f ( j < i ) goto 5
temp = arr ( i )
a r r ( i ) = ar r ( j )
a r r ( j ) = temp
tempb = brr ( i )
brr ( i ) = brr ( j )
brr ( j ) = tempb
goto 3
5 ar r ( l +1) = ar r ( j )
a r r ( j ) = a
brr ( l +1) = brr ( j )
brr ( j ) = b
j s t a c k = j s t a c k+2
i f ( j s t a c k > NSTACK) pause ’NSTACK too smal l in sort2 ’
i f ( i r−i+1 >= j−l ) then
i s t a c k ( j s t a c k ) = i r
i s t a c k ( j s tack −1) = i
i r = j−1
e l s e
i s t a c k ( j s t a c k ) = j−1
i s t a c k ( j s tack −1) = l
l = i
end i f
end i f
goto 1
end subrout ine so r t 2
end module a r r a y t o o l s
213
Listing A.9: Input Parameters
200 n b % number o f a s s e t g r id po in t s
30 n y % number o f endowment g r id po in t s
1000 n samples % number o f samples in s imu la t i on
1500 n pe r i od s % number o f pe r i od s f o r each sample in
%s imu la t i on
0 .90 beta % di scount f a c t o r
2 . 0 sigma % r i s k ave r s i on
0 .01 r % r i s k f r e e ra t e
0 .95 rho % p e r s i s t e n c e o f output
0 .027 s igma e % std dev o f innovat ion to output
0 .083 lambda % output pena l ty i f d e f a u l t
0 .222222 tauL % tax rate , low type
0 .50 tauH % tax rate , high type
0 .040 piL % prob o f turnover , low type
0 .040 piH % prob o f turnover , high type
−0.12 b min % minimum a s s e t p o s i t i o n
0 .0 b max % maximum a s s e t p o s i t i o n
1 .0 b s c a l e % c o n t r o l s i n t e r v a l between a s s e t g r id
% po in t s
3 . 0 y width % range o f y = [ mean − y width∗ sd y ,
5 mean + y width∗ sd y ]
214
0 new v0 % i f = 1 , i n i t i a l i z e va lue f u n c t i o n s
%with 0 , i f = 0 , i n i t i a l i z e va l
% gues s v ∗ . tx t f i l e s
215
A.1.3 MATLAB CODES
These Matlab codes then use the data from the value function iteration and the
model simulation to do the various plots and estimation of statistics. The code
plot results statistics.m uses the Matlab function read data.m to import the data.
Listing A.10: Matlab Codes for plots and statistics
%SELECT 1000SAMPLES OF 32 PERIODS FROM 1500 PERIODS TO MATCH. .
% NIGERIA. No r e s t r i c t i o n on d e f a u l t
%This code c a l c u l a t e s the s t a t i s t i c s used in the second . . . . .
%chapter o f the t h e s i s
c l e a r a l l
c l o s e a l l
c l c
% get parameters
p = read data ( ’ params . txt ’ ) ;
% get va lue f u n c t i o n s and p o l i c y f u n c t i o n s
v = read data ( ’ v f i d a t a . txt ’ )
% get s imu la t i on data
d = read data ( ’ s im data . txt ’ )
fn = 0 ;
% value func t i on : v (b , y , h , type )
[ n b , n y , n h , n t ] = s i z e ( v . v ) ;
%samples and pe r i od s
[ n per iods , n sample ] = s i z e (d . sim b ) ;
%PLOT
fn = fn +1; f i g u r e ( fn ) ; c l f ;
i b 2 = round (0 . 5∗ n b ) ;
hold on
p lo t ( v . y gr id , −squeeze ( v . bn( i b2 , : , 1 , 1 ) ) , ’ b− ’ , ’ LineWidth ’ , 2 )
hold o f f
x l a b e l ( ’ endowment , l og y ’ )
216
y l a b e l ( ’−b ’ ’ ’ )
t i t l e ( ’−b ’ ’ p o l i c y funct ion , h = 0 , low type ’ )
l e g = s p r i n t f ( ’ b = %f ’ , v . b g r i d ( i b 2 ) ) ;
l egend ( l e g )
% be f o r e computing s imu la t i on averages
% drop i n i t i a l 200 obs e rva t i on s f o r each sample
T0 = 200 ;
sim q = d . sim q (T0+1:end , : ) ;
sim pd = d . sim pd (T0+1:end , : ) ;
s im d = d . sim d (T0+1:end , : ) ;
s im type = d . s im type (T0+1:end , : ) ;
n pe r i od s = n pe r i od s − T0 ;
sim y = log (d . s im output (T0+1:end , : ) ) ;
sim bn = d . sim bn (T0+1:end , : ) ;
s im c = log (d . s im c (T0+1:end , : ) ) ;
%c a l c u l a t i n g trade balance
s im tau = ze ro s ( s i z e ( s im type ) ) ;
s im tau ( s im type == 1) = p . tauL ;
s im tau ( s im type == 2) = p . tauH ;
sim yy=(d . s im output (T0+1:end , : ) ) ;
s im cc=(d . s im c (T0+1:end , : ) ) ;
tb y = ((1− s im tau ) . ∗ sim yy − s im cc ) . / sim yy ;
%c a l c u l a t i n g spread
s im r = 1 ./ sim q − 1 ; % i n t e r e s t r a t e
cs = s im r − p . r ; % c r e d i t spread
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%expected d e f a u l t from change in type
ch L to H de f au l t = ( s im type ( 1 : end−1 , : ) == 1 & sim type ( 2 : . . .
end , : ) == 2 & sim d ( 2 : end ,:)== 1 ) ;
ch L to H = ( s im type ( 1 : end−1 , : ) == 1 & sim type ( 2 : . . .
end , : ) == 2 ) ;
ch H to L de f au l t = ( s im type ( 1 : end−1 , : ) == 2 & sim type ( 2 : . . .
end , : ) == 1 & sim d ( 2 : end ,:)== 1 ) ;
ch H to L = ( s im type ( 1 : end−1 , : ) == 2 & sim type ( 2 : . . .
217
end , : ) == 1 ) ;
num L to H defaults = sum(sum( ch L to H de f au l t ) ) ;
num L to H = sum(sum( ch L to H ) ) ;
L t o H d e f r a t e = num L to H defaults / num L to H
num H to L defaults = sum(sum( ch H to L de f au l t ) ) ;
num H to L = sum(sum( ch H to L ) ) ;
H t o L d e f r a t e = num H to L defaults / num H to L
%S e l e c t data when f o r only l e s s corrupt
f o r j =0:39
h=32;
f o r m=1:1000;
i f s im type ( j ∗h+1:( j +1)∗h ,m)==1
yolo L ( : ,m) =sim y ( j ∗h+1:( j +1)∗h ,m) ;
type L ( : ,m) =sim type ( j ∗h+1:( j +1)∗h ,m) ;
co lo L ( : ,m) =sim c ( j ∗h+1:( j +1)∗h ,m) ;
c s o l o L ( : ,m) =cs ( j ∗h+1:( j +1)∗h ,m) ;
tb yo lo L ( : ,m)=tb y ( j ∗h+1:( j +1)∗h ,m) ;
D L ( : ,m) =sim d ( j ∗h+1:( j +1)∗h ,m) ;
pd L ( : ,m) =sim pd ( j ∗h+1:( j +1)∗h ,m) ;
end
end
end
%S e l e c t data when f o r only more corrupt
f o r j =0:39
h=32;
f o r m=1:1000;
i f s im type ( j ∗h+1:( j +1)∗h ,m)==2
yolo H ( : ,m) =sim y ( j ∗h+1:( j +1)∗h ,m) ;
type H ( : ,m) =sim type ( j ∗h+1:( j +1)∗h ,m) ;
colo H ( : ,m) =sim c ( j ∗h+1:( j +1)∗h ,m) ;
cso lo H ( : ,m) =cs ( j ∗h+1:( j +1)∗h ,m) ;
tb yo lo H ( : ,m)=tb y ( j ∗h+1:( j +1)∗h ,m) ;
D H ( : ,m) =sim d ( j ∗h+1:( j +1)∗h ,m) ;
218
pd H ( : ,m) =sim pd ( j ∗h+1:( j +1)∗h ,m) ;
end
end
end
%S e l e c t data f o r both types−uncond i t i ona l
f o r j =0:39
h=32;
f o r m=1:1000;
yolo U ( : ,m) =sim y ( j ∗h+1:( j +1)∗h ,m) ;
type U ( : ,m) =sim type ( j ∗h+1:( j +1)∗h ,m) ;
colo U ( : ,m) =sim c ( j ∗h+1:( j +1)∗h ,m) ;
cso lo U ( : ,m) =cs ( j ∗h+1:( j +1)∗h ,m) ;
tb yo lo U ( : ,m)=tb y ( j ∗h+1:( j +1)∗h ,m) ;
D U ( : ,m) =sim d ( j ∗h+1:( j +1)∗h ,m) ;
pd U ( : ,m) =sim pd ( j ∗h+1:( j +1)∗h ,m) ;
end
end
%HP f i l t e r i n g data f o r quar t e r s
lambda = 1600 ;
%l e s s corrupt
y trend L = h p f i l t e r ( yolo L , lambda ) ;
yy dev L = yolo L−y trend L ;
s td y L = mean( std ( yy dev L ) )∗1 0 0 ;
c t r end L = h p f i l t e r ( co lo L , lambda ) ;
c dev L = colo L−c t r end L ;
s td c L = mean( std ( c dev L ) )∗1 0 0 ;
c s t r end L = h p f i l t e r ( cso lo L , lambda ) ;
c s dev L = cso lo L−c s t r end L ;
s t d c s L = mean( std ( cs dev L ) )∗1 0 0 ;
tb t rend L = h p f i l t e r ( tb yo lo L , lambda ) ;
tb dev L = tb yolo L−tb t rend L ;
219
s td tb L = mean( std ( tb dev L ) )∗1 0 0 ;
%%%%%%c o r r r e l a t i o n s
c o r r y c L=c o r r c o e f ( yy dev L , c dev L ) ;
c o r r y t b L=c o r r c o e f ( yy dev L , tb dev L ) ;
c o r r y c s L=c o r r c o e f ( yy dev L , cs dev L ) ;
c o r r t b c s L=c o r r c o e f ( tb dev L , cs dev L ) ;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%more corrupt
y trend H = h p f i l t e r ( yolo H , lambda ) ;
yy dev H= yolo H−y trend H ;
std y H= mean( std ( yy dev H ) )∗1 0 0 ;
c trend H = h p f i l t e r ( colo H , lambda ) ;
c dev H= colo H−c trend H ;
std c H= mean( std ( c dev H ) )∗1 0 0 ;
c s t rend H = h p f i l t e r ( csolo H , lambda ) ;
cs dev H= csolo H−cs t rend H ;
s td cs H= mean( std ( cs dev H ) )∗1 0 0 ;
tb trend H = h p f i l t e r ( tb yolo H , lambda ) ;
tb dev H= tb yolo H−tb trend H ;
std tb H= mean( std ( tb dev H ) )∗1 0 0 ;
%c o r r e l a t i o n
co r r y c H=c o r r c o e f ( yy dev H , c dev H ) ;
co r r y tb H=c o r r c o e f ( yy dev H , tb dev H ) ;
c o r r y c s H=c o r r c o e f ( yy dev H , cs dev H ) ;
c o r r t b c s H=c o r r c o e f ( tb dev H , cs dev H ) ;
%%%%%%%UNCONDITIONAL
y trend U = h p f i l t e r ( yolo U , lambda ) ;
yy dev U= yolo U−y trend U ;
std y U= mean( std ( yy dev U ) )∗1 0 0 ;
c trend U = h p f i l t e r ( colo U , lambda ) ;
c dev U= colo U−c trend U ;
220
s td c U= mean( std ( c dev U ) )∗1 0 0 ;
c s t rend U = h p f i l t e r ( csolo U , lambda ) ;
cs dev U= csolo U−cs t rend U ;
s td cs U= mean( std ( cs dev U ) )∗1 0 0 ;
tb trend U = h p f i l t e r ( tb yolo U , lambda ) ;
tb dev U= tb yolo U−tb trend U ;
std tb U= mean( std ( tb dev U ) )∗1 0 0 ;
%%%%%%c o r r r e l a t i o n
co r r y c U=c o r r c o e f ( yy dev U , c dev U ) ;
co r r y tb U=c o r r c o e f ( yy dev U , tb dev U ) ;
c o r r y c s U=c o r r c o e f ( yy dev U , cs dev U ) ;
c o r r t b c s U=c o r r c o e f ( tb dev U , cs dev U ) ;
%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%
% Credit Spreads
% mean c r e d i t spread , o v e r a l l
% get c r e d i t spreads f o r the types
mean cs = 4∗100∗mean(mean( cso lo U ) ) ; % annual
cs L = cso l o L ;
cs H = cso lo H ;
mean cs L = 4∗100∗mean(mean( cs L ));% annual
mean cs H = 4∗100∗mean(mean( cs H ));% annual
%%%%%%%%%%%%%%%%%%%%%%%
% Defau l t P r o b a b i l i t i e s
%%%%%%%%%%%%%%%%%%%%%%%
% mean d e f a u l t p robab i l i t y , o v e r a l l
% d e f a u l t p r o b a b i l i t i e s by type
mean pd = 4∗100 ∗ mean(mean ( ( pd U ))) ;% annual
mean pd L = 4∗100∗mean(mean( pd L ));% annual
mean pd H = 4∗100∗mean(mean( pd H));% annual
%%%%%%%%%%%%%%%%%%%%%%%
% Avg # of Defau l t Occurrences Every Year
%%%%%%%%%%%%%%%%%%%%%%%
221
% mean d e f a u l t s per year (4 pe r i od s per year )
% d e f a u l t s by type
% mean d e f a u l t s per year (4 per year )
mean D = 4∗100 ∗ mean(mean(D U));% annual
mean D L = 4∗100 ∗ mean(mean(D L));% annual
mean D H = 4∗100 ∗ mean(mean(D H));% annual
%s t a t i s t i c s
s t a t s = {} ;
s t a t s . mean cs = mean cs ;
s t a t s . mean cs L = mean cs L ;
s t a t s . mean cs H = mean cs H ;
s t a t s . mean pd = mean pd ;
s t a t s . mean pd L = mean pd L ;
s t a t s . mean pd H = mean pd H ;
s t a t s . mean D = mean D ;
s t a t s . mean D L = mean D L ;
s t a t s . mean D H = mean D H ;
s t a t s
%s t a t i s t i c s l e s s cor rupt
s t a t s L = {} ;
s t a t s L . s td y L = std y L ;
s t a t s L . s td c L = std c L ;
s t a t s L . s t d c s L = 4∗ s t d c s L ;
s t a t s L . s td tb L = std tb L ;
s t a t s L . c o r r y c L = c o r r y c L ( 1 , 2 ) ;
s t a t s L . c o r r y c s L = c o r r y c s L ( 1 , 2 ) ;
s t a t s L . c o r r y t b L = c o r r y t b L ( 1 , 2 ) ;
s t a t s L . c o r r t b c s L = c o r r t b c s L ( 1 , 2 ) ;
s t a t s L
%s t a t i s t i c s more corrupt
s ta t s H = {} ;
s ta t s H . std y H = std y H ;
s ta t s H . std c H = std c H ;
222
s ta t s H . s td cs H = 4∗ s td cs H ;
s ta t s H . std tb H = std tb H ;
s ta t s H . co r r y c H = cor r y c H ( 1 , 2 ) ;
s ta t s H . c o r r y c s H = c o r r y c s H ( 1 , 2 ) ;
s ta t s H . co r r y tb H = cor r y tb H ( 1 , 2 ) ;
s ta t s H . c o r r t b c s H = c o r r t b c s H ( 1 , 2 ) ;
s ta t s H
%s t a t i s t i c s uncond i t i ona l on type
s ta t s U = {} ;
s ta t s U . std y U = std y U ;
s ta t s U . std c U = std c U ;
s ta t s U . s td cs U = 4∗ s td cs U ;
s ta t s U . std tb U = std tb U ;
s ta t s U . co r r y c U = cor r y c U ( 1 , 2 ) ;
s ta t s U . c o r r y c s U = c o r r y c s U ( 1 , 2 ) ;
s ta t s U . co r r y tb U = cor r y tb U ( 1 , 2 ) ;
s ta t s U . c o r r t b c s U = c o r r t b c s U ( 1 , 2 ) ;
s ta t s U
% c a l c u l a t e d e f a u l t s above long−run mean o f output .
DD L = sim d ( s im type == 1);% type−l e s s corrupt
DD H = sim d ( s im type == 2);% type−more corrupt
%d e f a u l t above long run mean
Y L = sim y ( s im type == 1);% type−l e s s corrupt
Y H = sim y ( s im type == 2);% type−more corrupt
D LA=DD L(Y L>0.0040);% above long−run mean o f output
D LB=DD L(Y L<=0.0040); d e f a u l t s %below mean output
DefLA=(sum(D LA)/sum(DD L))∗100% l e s s co r ruptpercentage
D HA=DD H(Y H>0 .0040) ; %more corrupt d e f a u l t s above mean y
D HB=DD H(Y H<=0.0040);
DefHA=(sum(D HA)/sum(DD H))∗100% percentage
223
DA=sim d ( sim y >0.0040);% a l l d e f a u l t s above mean output
DefA=(sum(DA)/sum(sum( sim d )) )∗100
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%s e l e t speads be f o r e and a f t e r d e f a u l t
f o r m=1:1000
f o r j =5:1296;
i f s im d ( j ,m)==1
c s s ( : ,m)=cs ( j −4: j +4,m) ;
end
end
end
c s s ( : , a l l ( ˜any ( c s s ) , 1 ) ) = [ ] ;
% removes a l l colums with a l l ze ro
c s s1=mean( c s s ( : , : ) ˜ = 0 ) ;
c s s1=mean( css , 2 ) ;
c s s2=cs s1 . / c s s1 (1 ,1) ;% grow ra t e o f spread
fn = fn +1; f i g u r e ( fn ) ; c l f ;
hold on
p lo t ( c s s2 )
%s e l e t borrowing be f o r e and a f t e r d e f a u l t
f o r m=1:1000
f o r j =5:1296;
i f s im d ( j ,m)==1
bn ( : ,m)=sim bn ( j −4: j +4,m) ;
end
end
end
bn( : , a l l ( ˜any ( bn ) , 1 ) ) = [ ] ;
% removes a l l colums with a l l ze ro
bn1=mean(bn ( : , : ) ˜ = 0 ) ;
bn1=mean(bn , 2 ) ;
bn2=bn1 . / bn1 (1 ,1) ;% grow ra t e o f borrowing
fn = fn +1; f i g u r e ( fn ) ; c l f ;
hold on
p lo t ( bn2 )
224
%Defau l t space −mesh s i z e o f b i s small , need l a r g e s i z e o f b
dd1 = ( ( v . d ( : , : , 1 , 1 ) ) ) ;
dd2 = ( ( v . d ( : , : , 1 , 2 ) ) ) ;
fn = fn +1; f i g u r e ( fn ) ; c l f ;
hold on
colormap ( [ 1 1 1 ;0 0 0 ] )
s1=mesh ( v . b gr id , v . y gr id , dd1 ’ ) ;
a x i s ( [ min ( v . b g r i d ) ,max( v . b g r i d ) , min ( v . y g r i d ) ,max ( . . .
v . y g r i d ) , 0 , 1 ] ) ;
view ( 0 , 9 0 ) ;
alpha ( s1 , 0 . 5 ) ;%0 .5 i s gray
hold on
s2=mesh ( v . b gr id , v . y gr id , dd2 ’ ) ;
a x i s ( [ min ( v . b g r i d ) ,max( v . b g r i d ) , min ( v . y g r i d ) ,max ( . . .
v . y g r i d ) , 0 , 1 ] ) ;
view ( 0 , 9 0 ) ;
x l a b e l ( ’ Bond ’ , ’ FontSize ’ , 1 2 ) ;
y l a b e l ( ’ Output ’ , ’ FontSize ’ , 1 2 ) ;
alpha ( s2 , 0 .0) ;% 0 i s b lack
hold o f f
225
Listing A.11: Matlab function for importing simulated data for plots
func t i on [ args ] = read data ( f i l ename )
%READ DATA Reads data from text f i l e .
% READ DATA(FILENAME) re tu rn s a 1x1 c e l l array conta in ing a l l
%the data s to r ed in FILENAME. FILENAME i s assumed to s p e c i f y
%a text f i l e in which the data i s s to r ed in the same format as
%that used by READ DATA.
% Author : Patr i ck Macnamara
% https : // s i t e s . goog l e . com/ s i t e /pmacnama/
i f narg in ˜= 1
e r r o r ( ’ usage : [ a rgs ] = read data ( f i l ename ) ’ ) ;
end
args = {} ;
% fopen r e tu rn s f i d >= 0 i f s u c c e s s f u l , −1 i f not
f i d = fopen ( f i l ename , ’ r ’ ) ;
whi l e f e o f ( f i d ) == 0
% try to read name o f v a r i a b l e and number o f dimensions
C = text scan ( f id , ’%s %d ’ , 1 ) ;
% i f s u c c e s s f u l , then read r e s t o f data f o r t h i s v a r i a b l e
% i f unsucce s s fu l , then the re i s no more data to read
i f f e o f ( f i d ) == 0
% get v a r i a b l e name
arg name = C{1}{1} ;
% get number o f dimensions
nd = C{2} ;
% read r e s t o f i n f o
D = text scan ( f id , ’%d ’ , nd ) ;
d = D{1} ’ ;
% get number o f e lements in array
N = 1 ;
226
f o r i = 1 : nd
N = d( i ) ∗ N;
end
% read va lues :
row data = text scan ( f id , ’%f ’ , N) ;
i f ( numel ( row data {1}) == N)
a r g v a l = reshape ( row data {1} , d ) ;
e l s e
f c l o s e ( f i d ) ;
e r r o r ( ’ I n v a l i d number o f array e lements stored ’ ) ;
end
% s t o r e v a r i a b l e in s t r u c t
args . ( arg name ) = a r g v a l ;
end
end
% f c l o s e r e tu rn s 0 i f s u c c e s s f u l , −1 i f not
f c l o s e ( f i d ) ;
end
227
A.2 Chapter 3 Computer Codes
A.2.1 STATA CODES
Stata code used for the empirical results of this chapter of the thesis.
Listing A.12: Stata Do file
// import data l im i t ed en fo r c ement . dta//COUNTRY RE AND FE; f u l l sampleegen id = group ( country )tab year , gen ( yr )x t s e t country yearx t l i n e lnrgdp ENF// s s c i n s t a l l sutex , r e p l a c esutex lnrgdp ENF cred i tdepth , minmax
xtreg lnrgdp ENF, ree s t s t o e s t1
xt reg lnrgdp ENF, f ee s t s t o e s t2
xt reg lnrgdp cred i tdepth , ree s t s t o e s t3
xt reg lnrgdp cred i tdepth , f ee s t s t o e s t4
xt reg lnrgdp ENF cred i tdepth , ree s t s t o e s t5
xt reg lnrgdp ENF cred i tdepth , f ee s t s t o e s t6
xt reg lnrgdp ENF cred i tdepth ENFCREDIT, f ee s t s t o e s t7
xt reg lnrgdp ENF cred i tdepth ENFCREDIT, ree s t s t o e s t8
e s t tab e s t1 e s t2 e s t3 e s t4 e s t5 e s t6 e s t7 e s t8 us ing
//COUNTRY RE AND FE//USING 36 COUNTRIES
228
// import data l i m i t e d e n f o r c e m e n t s h o r t . dtax t s e t country yearx t l i n e lnrgdp ENF
xtreg lnrgdp ENF, ree s t s t o e s t1
xt reg lnrgdp ENF, f ee s t s t o e s t2
xt reg lnrgdp cred i tdepth , ree s t s t o e s t3
xt reg lnrgdp cred i tdepth , f ee s t s t o e s t4
xt reg lnrgdp ENF cred i tdepth , ree s t s t o e s t5
xt reg lnrgdp ENF cred i tdepth , f ee s t s t o e s t6
xt reg lnrgdp ENF cred i tdepth ENFCREDIT, f ee s t s t o e s t7
xt reg lnrgdp ENF cred i tdepth ENFCREDIT, ree s t s t o e s t8
e s t tab e s t1 e s t2 e s t3 e s t4 e s t5 e s t6 e s t7 e s t8 us ing
//TIME AND COUNTRY RE AND FE// use l im i t ed en fo r c ement . dta ; f u l l samplext reg lnrgdp ENF yr2− yr9 , ree s t s t o e s t1
xt reg lnrgdp ENF yr2−yr9 , f ee s t s t o e s t2
xt reg lnrgdp c r ed i tdepth yr2−yr9 , ree s t s t o e s t3
xt reg lnrgdp c r ed i tdepth yr2−yr9 , f ee s t s t o e s t4
xt reg lnrgdp ENF cred i tdepth yr2−yr9 , re
229
e s t s t o e s t5
xt reg lnrgdp ENF cred i tdepth yr2−yr9 , f ee s t s t o e s t6
xt reg lnrgdp ENF cred i tdepth ENFCREDIT yr2−yr9 , f ee s t s t o e s t7
xt reg lnrgdp ENF cred i tdepth ENFCREDIT yr2−yr9 , ree s t s t o e s t8
e s t tab e s t1 e s t2 e s t3 e s t4 e s t5 e s t6 e s t7 e s t8
//TIME AND COUNTRY RE AND FE// use l i m i t e d e n f o r c e m e n t s h o r t . dta ” , 36 c o u n t r i e sxt reg lnrgdp ENF yr2−yr9 , ree s t s t o e s t1
xt reg lnrgdp ENF yr2−yr9 , f ee s t s t o e s t2
xt reg lnrgdp c r ed i tdepth yr2−yr9 , ree s t s t o e s t3
xt reg lnrgdp c r ed i tdepth yr2−yr9 , f ee s t s t o e s t4
xt reg lnrgdp ENF cred i tdepth yr2−yr9 , ree s t s t o e s t5xt reg lnrgdp ENF cred i tdepth yr2−yr9 , f ee s t s t o e s t6
xt reg lnrgdp ENF cred i tdepth ENFCREDIT yr2−yr9 , f ee s t s t o e s t7
xt reg lnrgdp ENF cred i tdepth ENFCREDIT yr2−yr9 , ree s t s t o e s t8
e s t tab e s t1 e s t2 e s t3 e s t4 e s t5 e s t6 e s t7 e s t8
230
A.2.2 DYNARE CODES
We solve the Dynamic Stochastic General Equilibrium (theoretical) model in Dynare.
In doing this we use the equilibrium conditions in Section (3.3.2.6) and the steady state
in Appendix(3.5.6) as initial values. Below is the Dynare code for the model.
Listing A.13: Dynare code
%=====================================================%
%This s o l v e s the investment model
%=====================================================%
%K i s aggregate c a p i t a l
%ke i s e n t r e p r e n e u r i a l c a p i t a l
%H aggregate i s hou l seho ld labour
%He i s e n t r e n e u r i l a labour
% q i s p r i c e o f c a p i t a l
% n i s net worth
%i i s investment
% d e f a u l t omegabb thre sho ld
% e n t r e n e u r i a l consumption
% household consumption
% Welf i s w e l f a r e
% w i s household wage ra t e
% we i s e n t r e n e u r i a l wage ra t e
% Y aggregate output
%C i s t o t a l consumption
% r r e n t a l r a t e o f c a p i t a l
%Rb i s l end ing ra t e
%rpBANK r i s k premium of l e n d e r s
%l ev l e v e r a g e
%PHI bankruptcy
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%f entrepreneur ’ s share o f c a p i t a l output
% g lender ’ s share o f c a p i t a l output
% A pro du c t i v i t y
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
var K ke H He h q n i omegabb ce cc Welf Cc Ce w we Y r I
. . . C Bankrupcy Rb rpBANK lev PHI phi f g A;
varexo eA eN;% shocks
parameters alpha zeta beta de l t a varphi gamma eta S nu
. . mu p M rhoA StdeA StdeN zetaa Ass ;
alpha = 0 . 3 6 ; %share o f c a p i t a l
ze ta = 1−alpha −0.0001; %share o f household labour
beta = 0 . 9 9 ; %di scount ra t e
de l t a = 0 . 0 2 ; %d e p r e c i a t i o n ra t e
gamma = 0 . 9 1 ; % s u r v i v a l r a t e o f ent repreneur
eta = 0 . 1 ;
rhoA = 0 . 9 5 ;
StdeA = 0 . 0 1 ;
StdeN = 0 . 1 ;
S = 0 . 2 0 7 ;
nu = 3;%2.52 ;
mu = 0 . 1 5 0 ; %v e r i f i c a t i o n co s t parameter
p = pi ;
M = −.5∗S ˆ2 ;
rhoStdA = 0 . 8 3 ;
StdeStdA = 0 . 1 9 ;
Ass =1;
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varphi =.5 ;
zetaa =0.4;% l i m i t e d enforcement , ze ta
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%MODEL BLOCK
model ;
q∗ cc ˆ(−1) = beta ∗( cc (+1)ˆ(−1))∗(q(+1)∗(1− de l t a )+r (+1)) ;
%Euler equat ion
cc ˆ(−1) = nu/w;%consumption l e i s u r e
ke = i ∗ f − ce /q ;
n = we + ( ke (−1))∗(q∗(1− de l t a )+r ) − StdeN∗eN ;
K = (1−de l t a )∗K(−1) + I ∗(1−mu∗PHI ) ;
(1− eta )∗ cc + eta ∗ ce + eta ∗ i = Y;
q = ( beta∗gamma) ∗ ( r (+1) + q(+1)∗(1− de l t a ) )∗
. . . ( ( q(+1)∗ f (+1))/(1−q(+1)∗g (+1)) ) ;
q = 1/(1 − mu∗PHI − (mu∗phi )∗ f /(1−PHI)∗(1− zetaa ) ) ;
i = (1/(1−q∗g ) ) ∗ n ;
Y = A∗(K(−1)ˆ alpha )∗ (Hˆ zeta )∗ (Heˆ(1−alpha−zeta ) ) ;
r = alpha∗A∗(K(−1)ˆ( alpha −1))∗(Hˆ zeta )∗ (Heˆ(1−alpha−zeta ) ) ;
w = zeta ∗A∗(K(−1)ˆ alpha )∗ (Hˆ( zeta −1))∗(Heˆ(1−alpha−zeta ) ) ;
we=(1−alpha−zeta )∗A∗(K(−1)ˆ alpha )∗ (Hˆ zeta )∗Heˆ(−( alpha+zeta ) ) ;
H = (1− eta )∗h;%household labour
He = eta ;% e n t r e p r e n e u r i a l labour
Cc = (1− eta )∗ cc ; %household consumption
Ce = eta ∗ ce ; %e n t r e o r e n e u r i a l consumption
C = (1− eta )∗ cc + eta ∗ ce ; %aggregate consumption
I = eta ∗ i ;
Bankrupcy = PHI ;
Rb = ( q∗ i ∗omegabb∗(1− zetaa ) ) / ( i−n);% lend ing ra t e
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rpBANK = Rb − 1 ; % r i s k premium of l ende r /bank
l ev = ( i−n)/n ; %l e v e r a g e
l og (A) =rhoA∗ l og (A(−1)) + eA ;
PHI = normcdf ( ( l og ( omegabb)−M)/S ) ;
phi = normpdf ( ( l og ( omegabb)−M)/S) / ( omegabb∗S ) ;
g = (1− zetaa )∗ normcdf ( ( l og ( omegabb)−M)/S − S) − PHI∗mu +
. . . . (1− zetaa )∗(1−PHI)∗omegabb;% lender ’ s share
f = 1−mu∗PHI− g;% entrepreneur ’ s share o f c a p i t a l
Welf = log ( cc)+nu∗(1−h)+beta∗Welf (+1);% w e l f a r e
end ;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
i n i t v a l ;% i n i t i a l va lue s supp l i ed
omegabb = 0 .603892 ;
PHI = normcdf ( ( l og ( omegabb)−M)/S ) ;
phi = normpdf ( ( l og ( omegabb)−M)/S) / ( omegabb∗S ) ;
g = (1− zetaa )∗ normcdf ( ( l og ( omegabb)−M)/S − S) − PHI∗mu +
. . . (1− zetaa )∗(1−PHI)∗omegabb ;
f = 1−mu∗PHI− g ;
q = 1/(1 − mu∗PHI − (mu∗phi )∗ f /(1−PHI)∗(1− zetaa ) ) ;
r = q∗((1−beta∗(1− de l t a ) )/ beta ) ;
H = . 3 ;
He = eta ;
h = .3/(1− eta ) ;
K = ( alpha / r )ˆ(1/(1− alpha ) )∗Heˆ((1−alpha−zeta )/(1− alpha ) )∗
. . . ( Hˆ( zeta /(1−alpha ) ) ) ;
Y = (Kˆ alpha )∗ (Hˆ zeta )∗ (Heˆ(1−alpha−zeta ) ) ;
i = ( de l t a /( eta∗(1−mu∗0 . 0 1 ) ) )∗K;
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n = (1−g∗q)∗ i ;
ke = ( beta /q )∗ ( eta ∗n−(1−alpha−zeta )∗Y) ;
ce = q∗( f ∗ i−(ke/ eta ) ) ;
cc = (Y − eta ∗ ce − eta ∗ i )/(1− eta ) ;
A = 1 ;
w = nu∗ cc ;
Welf =−100;% we l f a r e
end ;
steady ;
check ;
shocks ;
var eA ; s t d e r r . 01 ;
%var eN ; s t d e r r 2 ;
end ;
s t o ch s imu l ( order =1, i r f =30, h p f i l t e r =1600);
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